Monday, November 29, 2010
Week 6 Prompt
How do you determine if a sequence is arithmetic or geometric? What are the rules for finding limits? Give examples of each.
Sunday, November 28, 2010
another freebie!
another freebie! haha, what else do i remeber that was easy....
these formula's, i'm pretty sure they are for when you have an angle that they want the sin or cos of but its not on the trig chart but its the sum or difference of two angles that ARE on the trig chart.
its all about sin and cos
sin(alpha +/- beta) = sinalphacosbeta+/-cosalphasinbeta
cos(alpha +/-beta) = cosalphacosbeta -/+sinalphasinbeta
they could as you to find the exact value of cos 75
and B-rob told us that you use the cos formula above and use two trig chart angles that add or subtract to give you the anlge they want.
so you know that 45 and 30 are both trig chart angles and they ADD to give you 75, so you go to your cos formula and plug in the first part for addition, then you can look further down the formula and see that if its addtion in the front, that it'll be subtraction in the back.
you plug it in and get
cos45cos30-sin45sin30
so you use your brain the remeber the trig chart and you know this
square root of two over 2 * 1/2 - square root of 3 over 2 * square root of 2 over 2which simplifies to square root of 2 + square root of 6 all over 4
but if they give you something like this
sin15cos15-cos15sin15
you can know from the formula and from the sign inbetween that you have to ADD these two angles, which is the other side of the formula.
so you get sin 30
which is 1/2
waaaaaahoooooooo
holidays are overrr:(
these formula's, i'm pretty sure they are for when you have an angle that they want the sin or cos of but its not on the trig chart but its the sum or difference of two angles that ARE on the trig chart.
its all about sin and cos
sin(alpha +/- beta) = sinalphacosbeta+/-cosalphasinbeta
cos(alpha +/-beta) = cosalphacosbeta -/+sinalphasinbeta
they could as you to find the exact value of cos 75
and B-rob told us that you use the cos formula above and use two trig chart angles that add or subtract to give you the anlge they want.
so you know that 45 and 30 are both trig chart angles and they ADD to give you 75, so you go to your cos formula and plug in the first part for addition, then you can look further down the formula and see that if its addtion in the front, that it'll be subtraction in the back.
you plug it in and get
cos45cos30-sin45sin30
so you use your brain the remeber the trig chart and you know this
square root of two over 2 * 1/2 - square root of 3 over 2 * square root of 2 over 2which simplifies to square root of 2 + square root of 6 all over 4
but if they give you something like this
sin15cos15-cos15sin15
you can know from the formula and from the sign inbetween that you have to ADD these two angles, which is the other side of the formula.
so you get sin 30
which is 1/2
waaaaaahoooooooo
holidays are overrr:(
hmm maryy.
so we do get two freebie blogs to go over whhhaatever we feel like correct?
well i'm gonna go over the easiest stuff i can think of.
sooo SOHCAHTOA everyone!
well i'm gonna go over the easiest stuff i can think of.
sooo SOHCAHTOA everyone!
sin(theta)=opposite/hypotenuse
cos(theta)=adjacent/hypotenuse
tan(theta)=opposite/adjacent
you can find all the parts of the triangle with just the ones on top, but if they ask for something specific like csc, sec, or cot,you go by this
csc(theta)=hypotenuse/opposite
sec(theta)=hypotenuse/adjacent
cot(theta)=adjacent/opposite
this will only work if you are given a RIGHT triangle, where the hypotenuse will be opposite of the right angle.
When you are given an angle and the right angle, you will go and find the other angle inside the triangle, but you should still always use the one you are given incase you have made a mistake, because if you made a mistake on that, your whole problem will be WRONG!
Example.
A=90 C=65 and a=18
you draw your triangle and use 180-90-65, to get your B angle.
then you use cos to find c
and you use sin, to get b
makeup blogggggg
this blog is from the week i missed because of swimming
section 13-2
this section is just about recorsive numbers in a sequence
tn-1 means previous term
tn-2 means two terms back
tn-3 means three terms back
recorsive means define in terms of what came before
find the 2nd and 3rd terms
they give you a starting number and a sequence
t1=7 tn=tn-1+1
brob said you look at tn-1 as the term before and not as anything minus 1
so you take your first number and you plug it in
you will get tn=4(7)+1
then you get 29
so then you plug that number in to get the next one
so you get tn=4(29)+1 which equals 117
you do that to find infinite numbers in a recorsive sequence
example number 2
they could ask you what was asked above or they could give you the numbers and ask you to write a recorsive definition. which means a formula!
so if they gave you 4,7,10,13
you can see that they are adding three
soo tn=tn-1=3
and you use that formula to find other numbers
Dom's blog
Chapter 13- 4
Limits
limits have rules:
If the top exponent is equal to the bottom exponent the answer is coefficient
If the top exponent is greater than the bottom exponent answer is +/- infinite
If the top exponent is less than the bottom exponent answer is 0
limits have rules:
If the top exponent is equal to the bottom exponent the answer is coefficient
If the top exponent is greater than the bottom exponent answer is +/- infinite
If the top exponent is less than the bottom exponent answer is 0
The examples are not cooperating so im moving on.
Chapter 7-1
Converting to Radians
This is very easy
This is very easy
formula to radians: pi/180
formula to degrees: 180/pi
ex. 2pi degrees
2 x 180 = 360 degrees (just get rid of the pi)
ex 2. 540 degrees to radians
540/180 = 3pi
formula to degrees: 180/pi
ex. 2pi degrees
2 x 180 = 360 degrees (just get rid of the pi)
ex 2. 540 degrees to radians
540/180 = 3pi
dylan's back to school blog...
I'm going to go over 13-2 Recursive Definitions
An example of recursive definitions(meaning pre-term):
tn-1
tn-2
tn-3
...
ex. Find the 3rd, 4th, and 5th terms given:
t1=7, tn=4tn-1+1
t2=4(7)+1
=29
t3=4(29)+1
=117
t4=4(117)+1
=469
t5=4(469)+1
=1877
ex. Give a recursive def. for
4,7,10,13
tn=tn-1+3
An example of recursive definitions(meaning pre-term):
tn-1
tn-2
tn-3
...
ex. Find the 3rd, 4th, and 5th terms given:
t1=7, tn=4tn-1+1
t2=4(7)+1
=29
t3=4(29)+1
=117
t4=4(117)+1
=469
t5=4(469)+1
=1877
ex. Give a recursive def. for
4,7,10,13
tn=tn-1+3
Helen's Blog
Section 7-1
Converting:
convert degrees to rads: x pi/180
convert rads to degrees: x 180/pi
Section 10-1
Formulas:
sin(A+/-B)=sinA cosB+/ -cosA sinB
cos(A+/-B)=cosA cosB-/+sinA sinB
Examples:
1) Find the exact value of cos 75
cos(45+30)=cos 45 cos 30+ sin 45 sin 30
= (sq. root 2/2)(sq. root 3/2) + (sq. root 2/2)(1/2)
= Sq. root 6 + sq.root 2/4
2)simplify: cos 90 cos 45+sin 90 sin 45
= cos(90-45)
=cos 45
=sq. root 2/2
Converting:
convert degrees to rads: x pi/180
convert rads to degrees: x 180/pi
Section 10-1
Formulas:
sin(A+/-B)=sinA cosB+/ -cosA sinB
cos(A+/-B)=cosA cosB-/+sinA sinB
Examples:
1) Find the exact value of cos 75
cos(45+30)=cos 45 cos 30+ sin 45 sin 30
= (sq. root 2/2)(sq. root 3/2) + (sq. root 2/2)(1/2)
= Sq. root 6 + sq.root 2/4
2)simplify: cos 90 cos 45+sin 90 sin 45
= cos(90-45)
=cos 45
=sq. root 2/2
kaitlyn's bloggggg
In this blogg i will go overrrr chapter 10 section 1 since it was realllyyyyyyy easyy and i actually understood it prettyy well. All we really needed to know in this section was our two formulas and you also had to make sure you knew your trig chart prettyy well toooo.
Formulas: sin(A+-B)=sinAcosB+-cosAsinB
cos(A+-B)=cosAcosB-+sinAcosB
Exampleeeee: Find the exact value of sin75
-sin(45+30)=sin45cos30+cos45sin30
-sin(75)=(squarerootof 2/2)(squarerootof 3/2)+(squarerootof 2/2)(1/2)
-sin(75)=(squarrootof6/4)+(squarerootof 2/4)
-sin(75)=(squarerootof 6)+(squarerootof 2)/4 <-----answerrrrr!
Exampleeeeee: Simplifyyy cos60cos30-sin60sin30
-cos(60+30)
-cos(90)
- 1 <---answerrrr!!!
Well thats myy bloggg for this weekendddddd, hope everyone had a greatt thanksgivingg holidayy!!!! (: (:
Formulas: sin(A+-B)=sinAcosB+-cosAsinB
cos(A+-B)=cosAcosB-+sinAcosB
Exampleeeee: Find the exact value of sin75
-sin(45+30)=sin45cos30+cos45sin30
-sin(75)=(squarerootof 2/2)(squarerootof 3/2)+(squarerootof 2/2)(1/2)
-sin(75)=(squarrootof6/4)+(squarerootof 2/4)
-sin(75)=(squarerootof 6)+(squarerootof 2)/4 <-----answerrrrr!
Exampleeeeee: Simplifyyy cos60cos30-sin60sin30
-cos(60+30)
-cos(90)
- 1 <---answerrrr!!!
Well thats myy bloggg for this weekendddddd, hope everyone had a greatt thanksgivingg holidayy!!!! (: (:
tori michelleee.
Im gonna go over section 11.1 because thats the only one i rememberrr.
In this section we learned how to convert polar to rectangular and how to convert polar to rectangular. To do this, you must know the following formulas:to convert to rectangular--x=rcos(theta) y=rsin(theta)to convert to polar--r=square root of x^2 + y^2 tan(theta)= y/x(r,(theta)) - polar form(x,y) - rectangular
Example 1:Give the polar point for (1,1)r=square root of 1^2 + 1^2 = 1
*first you use the polar formulatan(theta)= 1/1 = 1
*use tan(theta) y/xtheta=tan^-1(1) = 45
*find the inverse*
because tan is positive, find where tan is positive on the trig chart.
it is positive in quadrant 1 and 3 so your answers are 45 and 225
so you gett, (1, 45) ; (-1, 225)
In this section we learned how to convert polar to rectangular and how to convert polar to rectangular. To do this, you must know the following formulas:to convert to rectangular--x=rcos(theta) y=rsin(theta)to convert to polar--r=square root of x^2 + y^2 tan(theta)= y/x(r,(theta)) - polar form(x,y) - rectangular
Example 1:Give the polar point for (1,1)r=square root of 1^2 + 1^2 = 1
*first you use the polar formulatan(theta)= 1/1 = 1
*use tan(theta) y/xtheta=tan^-1(1) = 45
*find the inverse*
because tan is positive, find where tan is positive on the trig chart.
it is positive in quadrant 1 and 3 so your answers are 45 and 225
so you gett, (1, 45) ; (-1, 225)
Over the break post
10.1 formulas for cos(X+B) and sin(X+B)
cos(X+-B)= cosXcosB -+ sinXsinB
sin(X+-B)= sinXcosB+- cosXsinB
Example #1
Find the exact value
Cos75
cos(45+30) X=45 B=30
cos45cos30 - sin45sin30
cos75= the sqaure root of 6 minus the square root of 2 all over 4.
Example #2
Sin15
sin(45-30) X=45 B=30
sin45cos30 - cos45sin30
sin15= the sqaure root of 6 minus the square root of 2 all over 4
cos(X+-B)= cosXcosB -+ sinXsinB
sin(X+-B)= sinXcosB+- cosXsinB
Example #1
Find the exact value
Cos75
cos(45+30) X=45 B=30
cos45cos30 - sin45sin30
cos75= the sqaure root of 6 minus the square root of 2 all over 4.
Example #2
Sin15
sin(45-30) X=45 B=30
sin45cos30 - cos45sin30
sin15= the sqaure root of 6 minus the square root of 2 all over 4
lawrence's blog
in this part i will go over chapter 7 sections 1 and 2. they are very simple but you need to know these formulas because you do use them in all the other chapters. if you havent learned by now when b rob said you need to know all of this stuff im sure everyone knows now. anyway i will start go over these to sections
SECTION 1
two units of measure: degrees and radians
convert degrees to rads is x pi/180
convert rads to degrees is x 180/pi
coterminal angles +/- 360 or +/- 2pi if in rads
to convert to minutes and seconds.
to convert to minutes and seconds you just multiply by 60
to get them out of minutes and seconds its
x/60 + y/3600
examples:
1) 315 degrees convert to rads
315 x pi/180
=7pi/4
2) 25.335 degrees convert to minutes and seconds
.335 x60= 20.1
.1 x60= 6
25 degrees 20' 6"
SECTION 2
these are the formulas
s=r theta
k=1/2 r squared theta
k= 1/2 rs
know s=arc length r=radius theta= central angles and k=area of a sector
theta must also be in radians!!!!!!!
example
1) sector of a circle has arc length 6cm& 75cm squared. find its radius and the measure of its central angle
s= 6cm k=75
r=? theta=?
75= 1/2r(6)
75=3r now you divide by 3
r=25cm dont forget the units
now you use s=r theta
6=25(theta)
theta= 6/25 rads
i hope this helped some people who may not totally get this and i hope those who didnt finally have it and i hope everyone had a great holiday break.
SECTION 1
two units of measure: degrees and radians
convert degrees to rads is x pi/180
convert rads to degrees is x 180/pi
coterminal angles +/- 360 or +/- 2pi if in rads
to convert to minutes and seconds.
to convert to minutes and seconds you just multiply by 60
to get them out of minutes and seconds its
x/60 + y/3600
examples:
1) 315 degrees convert to rads
315 x pi/180
=7pi/4
2) 25.335 degrees convert to minutes and seconds
.335 x60= 20.1
.1 x60= 6
25 degrees 20' 6"
SECTION 2
these are the formulas
s=r theta
k=1/2 r squared theta
k= 1/2 rs
know s=arc length r=radius theta= central angles and k=area of a sector
theta must also be in radians!!!!!!!
example
1) sector of a circle has arc length 6cm& 75cm squared. find its radius and the measure of its central angle
s= 6cm k=75
r=? theta=?
75= 1/2r(6)
75=3r now you divide by 3
r=25cm dont forget the units
now you use s=r theta
6=25(theta)
theta= 6/25 rads
i hope this helped some people who may not totally get this and i hope those who didnt finally have it and i hope everyone had a great holiday break.
Feroz's Double Blog
Oh my damn. I haven't done any of these and it's like almost midnight.
Feroz's Blog: Part 1: Chapter 13: Section 4: Limits
Like with everything in math, limits have rules:
1.) If the top exponent is equal to the bottom exponent the answer is coefficient
2.) If the top exponent is greater than the bottom exponent answer is +/- infinite
3.) If the top exponent is less than the bottom exponent answer is 0
Not that hard to remember actually.
*So yeah, showing an example for this is not working out for me, like it looks really bad. So um, all you really need to know is the 3 rules above, and if the exponents are the same on the top and bottom use the coefficients, and you should be able to figure out which side is greater or if they're the same.
Part 2: Chapter 7: Section 1: Converting to Radians
Converting something to degrees or radians is extremely simple. If I could marry a lesson, it would probably be this one.
To radians: pi/180
To degrees: 180/pi
ex. 2pi to degrees
2 x 180 = 360 degrees (just get rid of the pi)
ex 2. 540 degrees to radians
540/180 = 3pi
There. I would go into more detail but my laptops dying. Not that you needed more detail. Yeah.
Feroz's Blog: Part 1: Chapter 13: Section 4: Limits
Like with everything in math, limits have rules:
1.) If the top exponent is equal to the bottom exponent the answer is coefficient
2.) If the top exponent is greater than the bottom exponent answer is +/- infinite
3.) If the top exponent is less than the bottom exponent answer is 0
Not that hard to remember actually.
*So yeah, showing an example for this is not working out for me, like it looks really bad. So um, all you really need to know is the 3 rules above, and if the exponents are the same on the top and bottom use the coefficients, and you should be able to figure out which side is greater or if they're the same.
Part 2: Chapter 7: Section 1: Converting to Radians
Converting something to degrees or radians is extremely simple. If I could marry a lesson, it would probably be this one.
To radians: pi/180
To degrees: 180/pi
ex. 2pi to degrees
2 x 180 = 360 degrees (just get rid of the pi)
ex 2. 540 degrees to radians
540/180 = 3pi
There. I would go into more detail but my laptops dying. Not that you needed more detail. Yeah.
Saturday, November 27, 2010
Nathan's turkey blog
It's Saturday, LSU just lost, im mad and bored, so I might as well get this blog over with so that I can do nothing tommorrow.
I am going to review chapter ten, sections one and two. These were probably the easiest sections since chapter 7.
In section 10-1, we couldn't use calculators, and we needed to know these two formulas:
cos(alpha+-beta)=cos(alpha)cos(beta)-+sin(alpha)sin(beta)
sin(alpha+-beta)=sin(alpha)cos(beta)+-cos(alpha)sin(beta)
Ex. Find the exact value of sin 15.
sin(45-30)=sin45cos30-cos45sin30
=√2/2(√3/2)-√2/2(1/2)
=√6-√2/4
cosπ/4 cosπ/4-sinπ/4 sinπ/4
=cos(π/4+π/4)=cos 2π/4=cosπ/2=0
Section 10-2 deals with the same kind of problem solving; the formulas you need to know is:
tan(alpha+beta)=tan(alpha)+tan(beta)/1-tan(alpha)tan(beta)
tan(alpha-beta)=tan(alpha)-tan(beta)/1+tan(alpha)tan(beta)
tan110-tan50/1+tan110tan50
=tan(110-50)
=tan60
=√3
tan27+tan18/1-tan27tan18
=tan(27+18)
=tan45
=1
Another easy section was 13-1. This section dealt with arithmetic and geometric sequences. An arithmetic sequence is when you add or subtract the numbers. A geometric sequence is when you multiply or divide to get the next number.
Ex. In a geometric sequence, t3=12 and t6=96, find t11
96/12=8
r^3=8
r=2
tn=3*2^11-1
t11=3*2^10
t11=3*1024
t11=3072
I am going to review chapter ten, sections one and two. These were probably the easiest sections since chapter 7.
In section 10-1, we couldn't use calculators, and we needed to know these two formulas:
cos(alpha+-beta)=cos(alpha)cos(beta)-+sin(alpha)sin(beta)
sin(alpha+-beta)=sin(alpha)cos(beta)+-cos(alpha)sin(beta)
Ex. Find the exact value of sin 15.
sin(45-30)=sin45cos30-cos45sin30
=√2/2(√3/2)-√2/2(1/2)
=√6-√2/4
cosπ/4 cosπ/4-sinπ/4 sinπ/4
=cos(π/4+π/4)=cos 2π/4=cosπ/2=0
Section 10-2 deals with the same kind of problem solving; the formulas you need to know is:
tan(alpha+beta)=tan(alpha)+tan(beta)/1-tan(alpha)tan(beta)
tan(alpha-beta)=tan(alpha)-tan(beta)/1+tan(alpha)tan(beta)
tan110-tan50/1+tan110tan50
=tan(110-50)
=tan60
=√3
tan27+tan18/1-tan27tan18
=tan(27+18)
=tan45
=1
Another easy section was 13-1. This section dealt with arithmetic and geometric sequences. An arithmetic sequence is when you add or subtract the numbers. A geometric sequence is when you multiply or divide to get the next number.
Ex. In a geometric sequence, t3=12 and t6=96, find t11
96/12=8
r^3=8
r=2
tn=3*2^11-1
t11=3*2^10
t11=3*1024
t11=3072
Nicala's Post
chapter 13 section 1
geometric and arithmetic sequences
arithmetic sequence is a sequence where the same number is added each time.
Formula: tn=t1+(n-1)d
geometric sequence is a sequence where the same number is multiplied each time.
Formula: tn=t1xr^n-1
Sample Problem
Find thed first four terms and state whether the sequences is arithmetic, geometric, or neither.
To find the first four terms, replace the n with 1.
Then 2, then 3, and 4.
tn=3n+2
tn=3(1)+2
tn=3+2
tn=5
tn=3n+2
tn=3(2)+2
tn=6+2
tn=8
tn=3n+2
tn=3(3)+2
tn=9+2
tn=11
tn=3n+2
tn=3(4)+2
tn=12+2
tn=14
Answer: 5,8,11,14
the sequence is arithmetic and d=3
geometric and arithmetic sequences
arithmetic sequence is a sequence where the same number is added each time.
Formula: tn=t1+(n-1)d
geometric sequence is a sequence where the same number is multiplied each time.
Formula: tn=t1xr^n-1
Sample Problem
Find thed first four terms and state whether the sequences is arithmetic, geometric, or neither.
To find the first four terms, replace the n with 1.
Then 2, then 3, and 4.
tn=3n+2
tn=3(1)+2
tn=3+2
tn=5
tn=3n+2
tn=3(2)+2
tn=6+2
tn=8
tn=3n+2
tn=3(3)+2
tn=9+2
tn=11
tn=3n+2
tn=3(4)+2
tn=12+2
tn=14
Answer: 5,8,11,14
the sequence is arithmetic and d=3
Friday, November 26, 2010
Taylor"s 12(I think) Blog
This is some of my notes from Ch. 13.1.
A sequence is a set of numbers. Today we will learn a bit about arithmetic sequence which is when you add the same number to every term.
This is the formula:
tn= t1 +(n-1)d
d is the number that is being added or subtracted. The n and one by the t are small to.
Ok let's do some examples.
Find the first 5 terms of this equation tn+ 6n+2
t1= 6(1)+2 First replace n with 1,2,3, and for and solve the equation.
t2=6(2)+2
t3=6(3)+2
t4=6(4)+2
t1= 8 Then you have your answers.
t2= 14
t3= 20
t4= 26
8,13,18,23.... find the formula for the nth term.
8,13,18,23.... First you need to figure out what is being added or subtracted from
each number. In this case it is adding 5.
tn=t1+(n-1)d Then write out your equation.
tn=8+(n-1)5 Then fill out the parts that you know2.
tn=8+5n-5 Then multiply 5 times n and -1.
tn= 3+ 5n Then you just add up your like terms and this is your answer.
These are some of my notes on Ch. 13.1. So UN TIL SCHOOL STARTS SEE YALL!!!
A sequence is a set of numbers. Today we will learn a bit about arithmetic sequence which is when you add the same number to every term.
This is the formula:
tn= t1 +(n-1)d
d is the number that is being added or subtracted. The n and one by the t are small to.
Ok let's do some examples.
Find the first 5 terms of this equation tn+ 6n+2
t1= 6(1)+2 First replace n with 1,2,3, and for and solve the equation.
t2=6(2)+2
t3=6(3)+2
t4=6(4)+2
t1= 8 Then you have your answers.
t2= 14
t3= 20
t4= 26
8,13,18,23.... find the formula for the nth term.
8,13,18,23.... First you need to figure out what is being added or subtracted from
each number. In this case it is adding 5.
tn=t1+(n-1)d Then write out your equation.
tn=8+(n-1)5 Then fill out the parts that you know2.
tn=8+5n-5 Then multiply 5 times n and -1.
tn= 3+ 5n Then you just add up your like terms and this is your answer.
These are some of my notes on Ch. 13.1. So UN TIL SCHOOL STARTS SEE YALL!!!
Wednesday, November 24, 2010
charlie's 2nd thanksgiving bloggy thinggy.
Okay, so a while back we learned how to turn polar form into rectangular form.
i forgot what chapter and section it's in though.
so.. the definition of polar is to graph using angles
polar form is (r, theta) and rectangular form is (x, y)
the formulas we used for this was...
r = `the square root of` x^2 + y^2
and
tantheta = (y/x)
[ this easily changes to theta = tangent inverse of (y/x) ]
so to do this you basically just plug in the (x, y) rectangular form numbers into the two formulas to get the (r, theta) polar form.
EXAMPLE:
#1. turn rectangular form (-1, 2) into polar form
[ first, you plug the -1 and the 2 into the formulas ]
r = `the square root of` -1^2 + 2^2
= `the square root of` 1 + 4
= +/- `the square root of` 5
theta = tangent inverse of (2/-1)
= 63.565
[ tangent is negative on the unit circle in quadrant 2 &4, so now you make 63 negative and add 180 & make 63 negative and add 360 to get to those quadrants ]
.... `the square root of` 5, 116. 565
.... `the square root of` -5, 296.565
i forgot what chapter and section it's in though.
so.. the definition of polar is to graph using angles
polar form is (r, theta) and rectangular form is (x, y)
the formulas we used for this was...
r = `the square root of` x^2 + y^2
and
tantheta = (y/x)
[ this easily changes to theta = tangent inverse of (y/x) ]
so to do this you basically just plug in the (x, y) rectangular form numbers into the two formulas to get the (r, theta) polar form.
EXAMPLE:
#1. turn rectangular form (-1, 2) into polar form
[ first, you plug the -1 and the 2 into the formulas ]
r = `the square root of` -1^2 + 2^2
= `the square root of` 1 + 4
= +/- `the square root of` 5
theta = tangent inverse of (2/-1)
= 63.565
[ tangent is negative on the unit circle in quadrant 2 &4, so now you make 63 negative and add 180 & make 63 negative and add 360 to get to those quadrants ]
.... `the square root of` 5, 116. 565
.... `the square root of` -5, 296.565
Week 6 Prompt
Due to the fact that the internet was not dependable on my laptop I was unable to post the blog prompt for the holidays. Therefore it is a freebie for everyone. Just make sure to post your 2 regular blogs. They can come from any review topic.
Sunday, November 21, 2010
What I learned this week.
This week was on chapter 13,
and there are many more sections and chapters to come.
This chapter had six sections,
and none of the six were fun.
But I learned something new,
and true knowledge I received.
More problems and more formulas,
seems to always keep my mind off ease.
This is the time of the year,
were high school kids always seems to slack off.
This is how teens go down the wrong path,
and the knowledge that was gained, ends up lost.
I tend to not follow the crowd,
and get lost in the struggle.
I plan to keep my grades up,
and stay away from trouble.
The week was long and tough,
but now we have a break.
Now I have time to catch up on sleep,
from those long nights of staying up late.
Happy holidays to everyone,
and have of mind full of love instead of hate.
And don't take this time for granted,
go to sleep instead of staying up eating thanksgiving cake.
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
torisss.
I don't know what to do this blog on so im just gonna do it on the same one i did last week.
This week we did chapter 13.
the chapter is about sequences, which are a listing of numbers.
Each sequence is either arithmetic (adding the same number every term) or geometric (multipling by the same number for every term).
For this we have two formulas:
arithmetic formula: t*n = t*1 + (n-1)d
geometric formula: t*n = t*1 X r^n-1
For these formulas d is the number being added or subtracted and r is the number being multiplied by.
Or you may have to find certain terms.
Fo this you get a formula like t*n = #n -# and you make n the term you're looking for.
Some Examples:
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
This week we did chapter 13.
the chapter is about sequences, which are a listing of numbers.
Each sequence is either arithmetic (adding the same number every term) or geometric (multipling by the same number for every term).
For this we have two formulas:
arithmetic formula: t*n = t*1 + (n-1)d
geometric formula: t*n = t*1 X r^n-1
For these formulas d is the number being added or subtracted and r is the number being multiplied by.
Or you may have to find certain terms.
Fo this you get a formula like t*n = #n -# and you make n the term you're looking for.
Some Examples:
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
Nathan's Blog
I am going to do this blog on section 13-4. These are the rules for fractions.
1.) If the top exponent is equal to the bottom exponent the answer is coefficient
2.) If the top exponent is greater than the bottom exponent answer is +- infinite
3.) If the top exponent is less than the bottom exponent answer is 0
Examples: All equations have lim/n→(infinite)
sin(1/n)=0
n^2+1/2n^2-3n=1/2 (exponents are equal; take coefficients)
7n^3/4n^2-5=infinite (top exponent is greater)
-n^2/n+1= -infinite
n+5/n=1
2n^4/6n^5+7=0
Now I will go over section 13-5 which deals with the sum of an infinite geometric series. The formula is: sn=t1/1-r
To write a repeating decimal as a fraction: number repeating/last place-1
ex. .4646=46/100-1=46/99
Find the sum of the infinite geometrice series.
9-6+4-....
r=-6/9=-2/3; 4/-6=-2/3
sn=9/1-(-2/3)=27/5
Write .5(repeating) as a fraction.
5/10-1=5/9
Overall, these sections were pretty easy. If you don't know your formulas, then you might have a little trouble with the sections in chapter 13. Happy Turkey Day.
1.) If the top exponent is equal to the bottom exponent the answer is coefficient
2.) If the top exponent is greater than the bottom exponent answer is +- infinite
3.) If the top exponent is less than the bottom exponent answer is 0
Examples: All equations have lim/n→(infinite)
sin(1/n)=0
n^2+1/2n^2-3n=1/2 (exponents are equal; take coefficients)
7n^3/4n^2-5=infinite (top exponent is greater)
-n^2/n+1= -infinite
n+5/n=1
2n^4/6n^5+7=0
Now I will go over section 13-5 which deals with the sum of an infinite geometric series. The formula is: sn=t1/1-r
To write a repeating decimal as a fraction: number repeating/last place-1
ex. .4646=46/100-1=46/99
Find the sum of the infinite geometrice series.
9-6+4-....
r=-6/9=-2/3; 4/-6=-2/3
sn=9/1-(-2/3)=27/5
Write .5(repeating) as a fraction.
5/10-1=5/9
Overall, these sections were pretty easy. If you don't know your formulas, then you might have a little trouble with the sections in chapter 13. Happy Turkey Day.
lawrences blog
im doing this blog on chapter 10 section 1. this chapter took me a little while to get but now i know how to do it and it is easy. it is really simple. you have to know the formulas and you have to know the trig chart. everything from chapter 7 and on you better know or you will be beat down by b-rob with her tests.
formulas:
cos(alpha +/- beta) cos alpha cos beta -/+ sin alpha sin beta
sin(alpha +/- beta) sin alpha cos beta +/- cos alspha sin beta
aplha and beta come from the trig chart and add or subtract to get the angle you are looking for
examples:
1)
cos(75)
alpha 45
cos 30
sin(45+30)= sin45 cos30- cos45 sin30
=square root of2/2 (square root of 2/2)- square root of 2/2(1/2)
square root of6/4- square root of 2/4
= square root of 6-2 all over 4 (final answer)
this is what i learned from chapter 10 section 1. hope this helps some people
formulas:
cos(alpha +/- beta) cos alpha cos beta -/+ sin alpha sin beta
sin(alpha +/- beta) sin alpha cos beta +/- cos alspha sin beta
aplha and beta come from the trig chart and add or subtract to get the angle you are looking for
examples:
1)
cos(75)
alpha 45
cos 30
sin(45+30)= sin45 cos30- cos45 sin30
=square root of2/2 (square root of 2/2)- square root of 2/2(1/2)
square root of6/4- square root of 2/4
= square root of 6-2 all over 4 (final answer)
this is what i learned from chapter 10 section 1. hope this helps some people
Friday, November 19, 2010
Charlie's.
Today we took notes on the 'captial sigma'.
This is in chapter 13, i think section 6.
She gave us the definition of a sigma; which is, a sigma is a series written in condensed form.
For this you have the little capital sigma sign (it looks like a weird E)
On top of it is #, at the bottom is n=#, and on the right side is f(x).
Where # is the limits of summation, n is the index, and f(x) is the summand.
Examples:
#1:
6
E 2(x)+4
x=2
So you just plug this into the summand [which is 2(x) +4] starting with 2 and ending at 6, adding them inbetween.
2(2)+4 + 2(3)+4 + 2(4)+4 + 2(5)+4 + 2(6)+4
= 8 + 10 + 12 + 14 + 16
= 60
#2:
3
E (3-p)^2
p=-1
(3+1)^2 + (3-0)^2 + (3-1)^2 + (3-2)^2 + (3-3)^2
= 4^2 + 3^2 + 2^2 + 1^2 + 0^2
= 16 + 9 + 4 + 1 + 0
=30
This is in chapter 13, i think section 6.
She gave us the definition of a sigma; which is, a sigma is a series written in condensed form.
For this you have the little capital sigma sign (it looks like a weird E)
On top of it is #, at the bottom is n=#, and on the right side is f(x).
Where # is the limits of summation, n is the index, and f(x) is the summand.
Examples:
#1:
6
E 2(x)+4
x=2
So you just plug this into the summand [which is 2(x) +4] starting with 2 and ending at 6, adding them inbetween.
2(2)+4 + 2(3)+4 + 2(4)+4 + 2(5)+4 + 2(6)+4
= 8 + 10 + 12 + 14 + 16
= 60
#2:
3
E (3-p)^2
p=-1
(3+1)^2 + (3-0)^2 + (3-1)^2 + (3-2)^2 + (3-3)^2
= 4^2 + 3^2 + 2^2 + 1^2 + 0^2
= 16 + 9 + 4 + 1 + 0
=30
Taylor's 12th (I think XD) Blog
These are the other half of my notes on Chapter 11.1.
We will be learning how to convert rectangular to polar.
Here are the formulas.
r= square root of x^2 + y^2 tan theta= y/x
polar is in (r,theta) form and rectangular is in (x,y) form.
Now let's work on some problems.
C
onvert (8,9) to polar.
r= square root of 8^2 + 9^2 tan theta= 9/8 First, write out your problem so that
it will match the formula that I gave you.
r= square root of 64 + 81 theta= tan^-1 (9/8) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.
r= square root of 145 theta= 48.366 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will leave this as your answer and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 48.366 degrees to quadrant three you would add 180 degrees and get 228.366 degrees as the answer.
So your answer for this question should look like this (square root of 145 , 48.366 degrees ) and ( - square root of 145 , 228.366 degrees).
Convert (10,12) to polar.
r= square root of 10^2 + 12^2 tan theta= 12/10 First, write out your problem so that it will match the formula that I gave you.
r= square root of 100 + 144 theta= tan^-1 (12/10) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.
r= square root of 244 theta= 50.194 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will factor out the four and get 2 square root of 61 and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 50.194 degrees to quadrant three you would add 180 degrees and get 230.194 degrees as the answer.
So your answer for this question should look like this ( 2 square root of 61, 50.194 degrees ) and ( - 2 square root of 61, 230.194 degrees).
That is the last half of my notes from Chapter 11.1.
SO UNTIL NEXT TIME JA NE!!!!! (Japanese for goodbye.)
We will be learning how to convert rectangular to polar.
Here are the formulas.
r= square root of x^2 + y^2 tan theta= y/x
polar is in (r,theta) form and rectangular is in (x,y) form.
Now let's work on some problems.
C
onvert (8,9) to polar.
r= square root of 8^2 + 9^2 tan theta= 9/8 First, write out your problem so that
it will match the formula that I gave you.
r= square root of 64 + 81 theta= tan^-1 (9/8) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.
r= square root of 145 theta= 48.366 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will leave this as your answer and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 48.366 degrees to quadrant three you would add 180 degrees and get 228.366 degrees as the answer.
So your answer for this question should look like this (square root of 145 , 48.366 degrees ) and ( - square root of 145 , 228.366 degrees).
Convert (10,12) to polar.
r= square root of 10^2 + 12^2 tan theta= 12/10 First, write out your problem so that it will match the formula that I gave you.
r= square root of 100 + 144 theta= tan^-1 (12/10) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.
r= square root of 244 theta= 50.194 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will factor out the four and get 2 square root of 61 and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 50.194 degrees to quadrant three you would add 180 degrees and get 230.194 degrees as the answer.
So your answer for this question should look like this ( 2 square root of 61, 50.194 degrees ) and ( - 2 square root of 61, 230.194 degrees).
That is the last half of my notes from Chapter 11.1.
SO UNTIL NEXT TIME JA NE!!!!! (Japanese for goodbye.)
Nicala's Blog
chapter 7 section 4
finding a reference angle
finding a reference angle
- find the quadrant the angle is in.
- determine if the trig function is postive or negative
- subtract 180 degrees from the angle until theta is between 0 and angle.
- if it is a trig chart angle plug in, if not leav it or plug in calculator.
Hint: evaluate means # answer unlesas otherwise specified.
Find tan inverse (1) without a calculator.
- put it on the coordinating plane
- subtract from 180
- keep subtracting until you get a answer between zero and ninety.
the answer is forty five degrees.
Monday, November 15, 2010
Week 5 Blog Prompt
What is a famous sequences and series? What is it used for and who discovered it? Everyone should find a different type.
Sunday, November 14, 2010
Dom's blog
Chapter 13-1
tsub2=4(2)-3=8-3=5
tsub3=4(3)-3=12-3=9
tsub4=4(4)-3=16-3=12
arithmetic +4
Sequences-
is a list of numbers. There are two kinds of sequences:
1) Arithmetic- +/- by the same number every term
2) Geometric- *// by the same number every term
is a list of numbers. There are two kinds of sequences:
1) Arithmetic- +/- by the same number every term
2) Geometric- *// by the same number every term
Ex: if tsubnl=4n-3, find the first 4 terms:
tsub1=4(1)-3=4-3=1tsub2=4(2)-3=8-3=5
tsub3=4(3)-3=12-3=9
tsub4=4(4)-3=16-3=12
arithmetic +4
Well, I'm done.
Malorie's Blog
13.1 Sequences
In this lesson, we learned the two different types of sequencing, Arithmetic and Geometric. Arithmetic is when you add the same number to every term. Geometric is when you multiply by the same number for every term.
The formula to find the nth term for Arithmetic is tn= t1 + (n - 1)d
Geometric is: tn= t1 x r^(n-1)
t= term n= last number of sequence r= what is being added or multipled d= what is being added or subtracted
Example 1:
If tn=4n-3 find the first 4 terms and say whether it is arithmetic, geometric, or neither.
t1= 4(1)-3= 1
t2=4(2)-3=5
t3=4(3)-3=9
t4=4(4)-3=13
Arithmetic because 4 is being added to every term
Example 2:
If tn=2n+3 find the first 4 terms and say whether it is arithmetic, geometric, or neither.
t1=2(1)+3=5
t2=2(2)+3=7
t3=2(3)+3=9
t4+2(4)+3=11
Arithmetic because 2 is being added to every term
In this lesson, we learned the two different types of sequencing, Arithmetic and Geometric. Arithmetic is when you add the same number to every term. Geometric is when you multiply by the same number for every term.
The formula to find the nth term for Arithmetic is tn= t1 + (n - 1)d
Geometric is: tn= t1 x r^(n-1)
t= term n= last number of sequence r= what is being added or multipled d= what is being added or subtracted
Example 1:
If tn=4n-3 find the first 4 terms and say whether it is arithmetic, geometric, or neither.
t1= 4(1)-3= 1
t2=4(2)-3=5
t3=4(3)-3=9
t4=4(4)-3=13
Arithmetic because 4 is being added to every term
Example 2:
If tn=2n+3 find the first 4 terms and say whether it is arithmetic, geometric, or neither.
t1=2(1)+3=5
t2=2(2)+3=7
t3=2(3)+3=9
t4+2(4)+3=11
Arithmetic because 2 is being added to every term
kldfjalkjdv
this week i wish i didn't skip thursday because i had soo much trouble on my homework that it wasn't even funny..
this week, we learned about chapter 13
this chapter is about sequences, which is a list of numbers, there are two kinds
Arithmetic- add the same number to every term
Geometric- multiply by the same number for each number
if you divide the numbers in a sequences and you find a like ratio, then its geometric
here are your formulas
arithmetic- t(n)=t1 +(n-1)d
geometric= t(n)=t1 x r ^n-1
where d is what is being added or subtracted and where r is what you are multiplying by
example=t(n)=4(n)-3 find the four first terms
t1=4(1)-3=1
t2=4(2)-3=5
t3=4(3))-3=9
t4=4(4)-3=13
and from this you can determine that it is an aritmetic sequence
example 2
3,7,11,15... find a formula for the nth term
you take your fomula(arithmetic)
you know that tn is the total number
you know that t1 is the first number in the sequence
and you know that d is the number being added or subtracted
you can tell you are adding by the information given
now you just plug in your formula
tn=3 +(n-1)4
then simplify
tn=3+4n-4
tn=4n-1
and there ya have it
i only have one example of this same process but with geometric and i can't do geometric,i needd some help tomorrow B-Robbbb
Dylan's Bloggity Blog
Sec. 13-1 Sequences
A sequence is a list of numbers. There are two kinds:
Arithmetic- +/- by the same number every term
Geometric- *// by the same number every term
Ex 6,4,2,0,... is Arithmetic
4,7,11,16,22,... is neither
To find the n^m term, you use these formulas:
Arithmetic- tn=t1+(n-1)d
Geometric- tn=t1*r
( d= the number that is used for A and G, the number being //+/-/*)
A sequence is a list of numbers. There are two kinds:
Arithmetic- +/- by the same number every term
Geometric- *// by the same number every term
Ex 6,4,2,0,... is Arithmetic
4,7,11,16,22,... is neither
To find the n^m term, you use these formulas:
Arithmetic- tn=t1+(n-1)d
Geometric- tn=t1*r
( d= the number that is used for A and G, the number being //+/-/*)
What did we learn this week?
These chapters we've learned,
made us think a great deal.
We have to go into deep thinking
to sought out whats real.
Formulas are hard
and questions seem impossible to do.
But this is a good test,
to see what kind of person are u.
You learn more than you think,
and even more when you don't complain,
your mind is your thoughts,
so your mind is going to change.
Make the right decisions
even if the right thing is too hard to do
because the wrong thing is easier
So do most challenging, and his plan will go through.
Continue to seek change
and let your mind feel at ease
keep your faith in God
and always believe.
This week's material was all on chapter 13.
Arithmetic= tn= t1(n-1)d
Geometric= t1 x r^n-1
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
I'm sleepy goodnight bloggers!
made us think a great deal.
We have to go into deep thinking
to sought out whats real.
Formulas are hard
and questions seem impossible to do.
But this is a good test,
to see what kind of person are u.
You learn more than you think,
and even more when you don't complain,
your mind is your thoughts,
so your mind is going to change.
Make the right decisions
even if the right thing is too hard to do
because the wrong thing is easier
So do most challenging, and his plan will go through.
Continue to seek change
and let your mind feel at ease
keep your faith in God
and always believe.
This week's material was all on chapter 13.
Arithmetic= tn= t1(n-1)d
Geometric= t1 x r^n-1
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
I'm sleepy goodnight bloggers!
tori's
this week, we learned chapter 13 section 1.
it was extremely easy in my opinion!
Sequences-a list of numbers
arithmetic- when you add/subtract the same number to every term
geometric- when you multiply/divide the same number for every term
ex. 1
are the following sequences arithmetic, geometric, or neither?
a. 4, 8, 12, 16,...------> arithmetic +4
b. 9, 27/2, 81/4,...----> geometric x3/2
to find the nth term of a sequence
FORMULAS:
arithmetic- tsubn=tsub1+(n-1)d
geometric- tsubn=tsub1xr^(n-1)
where d is what is being added or subtracted and r is what you are multiplying or dividing by.
example 2:
if tsubnl=4n-3, find the first 4 terms:
tsub1=4(1)-3=4-3=1
tsub2=4(2)-3=8-3=5
tsub3=4(3)-3=12-3=9
tsub4=4(4)-3=16-3=12
arithmetic +4
and there we gooo!
it was extremely easy in my opinion!
Sequences-a list of numbers
arithmetic- when you add/subtract the same number to every term
geometric- when you multiply/divide the same number for every term
ex. 1
are the following sequences arithmetic, geometric, or neither?
a. 4, 8, 12, 16,...------> arithmetic +4
b. 9, 27/2, 81/4,...----> geometric x3/2
to find the nth term of a sequence
FORMULAS:
arithmetic- tsubn=tsub1+(n-1)d
geometric- tsubn=tsub1xr^(n-1)
where d is what is being added or subtracted and r is what you are multiplying or dividing by.
example 2:
if tsubnl=4n-3, find the first 4 terms:
tsub1=4(1)-3=4-3=1
tsub2=4(2)-3=8-3=5
tsub3=4(3)-3=12-3=9
tsub4=4(4)-3=16-3=12
arithmetic +4
and there we gooo!
Charlie's.
This week we started chapter 13.
the chapter is about sequences, which are a listing of numbers.
Each sequence is either arithmetic (adding the same number every term) or geometric (multipling by the same number for every term).
For this we have two formulas:
arithmetic formula: t*n = t*1 + (n-1)d
geometric formula: t*n = t*1 X r^n-1
For these formulas d is the number being added or subtracted and r is the number being multiplied by.
Or you may have to find certain terms.
Fo this you get a formula like t*n = #n -# and you make n the term you're looking for.
Some Examples:
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
the chapter is about sequences, which are a listing of numbers.
Each sequence is either arithmetic (adding the same number every term) or geometric (multipling by the same number for every term).
For this we have two formulas:
arithmetic formula: t*n = t*1 + (n-1)d
geometric formula: t*n = t*1 X r^n-1
For these formulas d is the number being added or subtracted and r is the number being multiplied by.
Or you may have to find certain terms.
Fo this you get a formula like t*n = #n -# and you make n the term you're looking for.
Some Examples:
#1: Find the first 5 terms of t*n = 2n - 9
t*1 = 2(1) - 9 = 2 - 9 = - 7
t*2 = 2(2) - 9 = 4 - 9 = -5
t*3 = 2(3) - 9 = 6 - 9 = -3
t*4 = 2(4) - 9 = 8 - 9 = -1
t*5 = 2(5) - 9 = 10 - 9 = 1
#2: 2, 4, 6, 8, 10
t*n = t*1 + (n-1)d
t*n = 2 + (n-1)2
t*n = 2 + 2n -2
t*n = 2n
Feroz's Blog
I'll go over 13-1 since I don't think we did anything else did this week besides tests.
So um, I explained what the difference between arithmetic and geometric was in my last blog, so straight to the formulas.
If it's arithmetic: Tn = T1 + (n-1)d
If it's geometric: Tn = T1 x r^n-1
ex. If Tn = 2n + 1, find the first 4 terms.
T1 = 2(1) + 1 = 3
T2 = 5
T3 = 7
T4 = 9
It is a arithmetic sequence since you're adding two.
ex 2. 3, 8, 13, 18... find the Nth term.
It's arithmetic, so:
Tn = T1 + (n-1)d
= 3 + 5n -5
= 5n -2
That's it.
So um, I explained what the difference between arithmetic and geometric was in my last blog, so straight to the formulas.
If it's arithmetic: Tn = T1 + (n-1)d
If it's geometric: Tn = T1 x r^n-1
ex. If Tn = 2n + 1, find the first 4 terms.
T1 = 2(1) + 1 = 3
T2 = 5
T3 = 7
T4 = 9
It is a arithmetic sequence since you're adding two.
ex 2. 3, 8, 13, 18... find the Nth term.
It's arithmetic, so:
Tn = T1 + (n-1)d
= 3 + 5n -5
= 5n -2
That's it.
lawrence's blog
in this blog i will talk about chapter 13 section 1. it is a very easy chapter and it has been awhile since we had an easy section. it kinda gives us a break for awhile but im sure it will get harder, but anyway in this chapter it deals with arithmatic and geometric. artithmatic is when you add the number to every term. geometric is when you multiply by the same nymber for every term. all of this has to do with sequences which is just a list of numbers,
examples:
1) 3,7,11,15....... find a formula for the Nth term
tn= t1+ (n-1)d
tn= 3+(n-1)4
tn= 3+ 4n-1
tn= 4n-1
2) find the formula for the Nth term of 3
3, 9/2, 27/4
9/2 all over 3/1= 9/6= 3/2
27/4 all over 9/2= 3/2
tn= 3x(3/2) n-1
this is all that i learned in section 1 of chapter 13. it is really easy and if anyone needs help you can just ask me. well now im going do my math homework.
examples:
1) 3,7,11,15....... find a formula for the Nth term
tn= t1+ (n-1)d
tn= 3+(n-1)4
tn= 3+ 4n-1
tn= 4n-1
2) find the formula for the Nth term of 3
3, 9/2, 27/4
9/2 all over 3/1= 9/6= 3/2
27/4 all over 9/2= 3/2
tn= 3x(3/2) n-1
this is all that i learned in section 1 of chapter 13. it is really easy and if anyone needs help you can just ask me. well now im going do my math homework.
Kaitlyn's blogg
In this blog, i will go over chapter 13-1. This section was really easy for me because it deals with arithmatic and geometric sequences.
Arithmatic- when you add to get the next term
formula: tn=t1+(n-1)d
Geometric-when you multiply to get the next term
formula: tn=t1 x r^n-1
Examples: 2,7,12,17.........find a formula for the nth term
-tn=2+(n-1)5
-tn=2+5n-5
-tn=-3+5n <-----answer
Examples: 5,10,20,40...is this sequence geometric or arithmatic?
-10/5=2
-20/10=2
-40/20=2
geometic <-----answer
This section cant really get confusing, because its pretty straightforward. I'm sure that the following chapters will end up getting more complicated and confusing thoughhh
=
Arithmatic- when you add to get the next term
formula: tn=t1+(n-1)d
Geometric-when you multiply to get the next term
formula: tn=t1 x r^n-1
Examples: 2,7,12,17.........find a formula for the nth term
-tn=2+(n-1)5
-tn=2+5n-5
-tn=-3+5n <-----answer
Examples: 5,10,20,40...is this sequence geometric or arithmatic?
-10/5=2
-20/10=2
-40/20=2
geometic <-----answer
This section cant really get confusing, because its pretty straightforward. I'm sure that the following chapters will end up getting more complicated and confusing thoughhh
=
Friday, November 12, 2010
Week 4 prompt
What trig concept do you feel most comfortable with from Ch. 9-11? Give an example w/an explanation of how it is worked.
All of the trig concepts are pretty difficult to me but the one i feel most comfortable with is chapter 10.1
10.1 formulas for cos(X+B) and sin(X+B)
cos(X+-B)= cosXcosB -+ sinXsinB
sin(X+-B)= sinXcosB+- cosXsinB
Example #1
Find the exact value
Cos75
cos(45+30) X=45 B=30
cos45cos30 - sin45sin30
cos75= the sqaure root of 6 minus the square root of 2 all over 4.
Example #2
Sin15
sin(45-30) X=45 B=30
sin45cos30 - cos45sin30
sin15= the sqaure root of 6 minus the square root of 2 all over 4
I would of wrote some more but I'm going to be real, its the weekend.
I'm just tryna chill you know what im sayin!! and plus i have sunday's blog tooo!!
All of the trig concepts are pretty difficult to me but the one i feel most comfortable with is chapter 10.1
10.1 formulas for cos(X+B) and sin(X+B)
cos(X+-B)= cosXcosB -+ sinXsinB
sin(X+-B)= sinXcosB+- cosXsinB
Example #1
Find the exact value
Cos75
cos(45+30) X=45 B=30
cos45cos30 - sin45sin30
cos75= the sqaure root of 6 minus the square root of 2 all over 4.
Example #2
Sin15
sin(45-30) X=45 B=30
sin45cos30 - cos45sin30
sin15= the sqaure root of 6 minus the square root of 2 all over 4
I would of wrote some more but I'm going to be real, its the weekend.
I'm just tryna chill you know what im sayin!! and plus i have sunday's blog tooo!!
Nathan's Blog
This is Nathan with the blog for the weekend.
The concept that I felt most comfortable with is section 13-1. This is probably the easiest section since chapter seven.This section deals with sequences, which is a list of numbers. The two answers that you can have is either arithmetic, or geometric. Arithmetic is when you add the same number to every term. Geometric is when you multiply the same number for every term.
Ex. 4,8,12,16- Arithmetic
9,27/2,81/4...- Geometric
These are examples of when you have to find the first four terms of each sequence. All you have to do is, plug 1,2,3,and 4 into each formula for n, and then determine if the answers give an arithmetic or geometric sequence.
tn=2n+3
t1=2*1+3=5
t2=2*2+3=7
t3=2*3+3=9
t4=2*4+3=11
This would be arithmetic because you are adding 2 to each term.
tn=3*2^n
t1=3*2^1=6
t2=3*2^1=12
t3=3*2^3=24
t4=3*2^4=48
This would be geometric because you are multiplying 2 to each equation.
That's it. Like I said, this is one of the easiest sections, but it's probably going to get tougher, like every other chapter in that book.
The concept that I felt most comfortable with is section 13-1. This is probably the easiest section since chapter seven.This section deals with sequences, which is a list of numbers. The two answers that you can have is either arithmetic, or geometric. Arithmetic is when you add the same number to every term. Geometric is when you multiply the same number for every term.
Ex. 4,8,12,16- Arithmetic
9,27/2,81/4...- Geometric
These are examples of when you have to find the first four terms of each sequence. All you have to do is, plug 1,2,3,and 4 into each formula for n, and then determine if the answers give an arithmetic or geometric sequence.
tn=2n+3
t1=2*1+3=5
t2=2*2+3=7
t3=2*3+3=9
t4=2*4+3=11
This would be arithmetic because you are adding 2 to each term.
tn=3*2^n
t1=3*2^1=6
t2=3*2^1=12
t3=3*2^3=24
t4=3*2^4=48
This would be geometric because you are multiplying 2 to each equation.
That's it. Like I said, this is one of the easiest sections, but it's probably going to get tougher, like every other chapter in that book.
Taylor's 11th (I think) Blog
These are half of my notes on Chapter 11.1.
We will be learning how to convert polar to rectangular.
Here are the formulas.
x= r x costheta y=r x sintheta
polar is in (r,theta) form and rectangular is in (x,y) form.
Now let's work on some problems.
Convert (5, 45 degrees) to rectangular.
x= 5 x cos 45 degrees y= 5 x sin 45 degrees First, write out your problem so that it will match the formula that I gave you.
x=5 x square root of 2/2 y=5 x square root of 2/2 Then if you can or want to simply use your trig chart for the sin and cos.
x= 3.536 y= 3.536 Finally you just need to multiply and you get this as your answer after you round to the third space after the decimal.
So (3.536, 3.536) is your answer for this question.
Let's do one more example.
Convert (8, 60 degrees) to rectangular.
x= 8 x cos 60 degrees y= 8 x sin 60 degrees First, write out your problem so that it will match the formula that I gave you.
x=8 x 1/2 y=8 x square root of 3/2 Then if you can or want to simply use your trig chart for the sin and cos.
x= 4 y= 6.928 Finally you just need to multiply and you get this as your answer after you round to the third space after the decimal for the y.
So (4, 6.928) is your answer for this question.
That is half of my notes from Chapter 11.1.
SO UNTIL NEXT TIME JA NE!!!!! (Japanese for goodbye.)
We will be learning how to convert polar to rectangular.
Here are the formulas.
x= r x costheta y=r x sintheta
polar is in (r,theta) form and rectangular is in (x,y) form.
Now let's work on some problems.
Convert (5, 45 degrees) to rectangular.
x= 5 x cos 45 degrees y= 5 x sin 45 degrees First, write out your problem so that it will match the formula that I gave you.
x=5 x square root of 2/2 y=5 x square root of 2/2 Then if you can or want to simply use your trig chart for the sin and cos.
x= 3.536 y= 3.536 Finally you just need to multiply and you get this as your answer after you round to the third space after the decimal.
So (3.536, 3.536) is your answer for this question.
Let's do one more example.
Convert (8, 60 degrees) to rectangular.
x= 8 x cos 60 degrees y= 8 x sin 60 degrees First, write out your problem so that it will match the formula that I gave you.
x=8 x 1/2 y=8 x square root of 3/2 Then if you can or want to simply use your trig chart for the sin and cos.
x= 4 y= 6.928 Finally you just need to multiply and you get this as your answer after you round to the third space after the decimal for the y.
So (4, 6.928) is your answer for this question.
That is half of my notes from Chapter 11.1.
SO UNTIL NEXT TIME JA NE!!!!! (Japanese for goodbye.)
Nicala's Blog
in chapter 13 section 1 we are learning sequences. there are two different types of sequences, arithmetic and geometric. if it is not a arithmetic or geometric then it is nether because it does not have follow sequences.
2, 6, 18, 54, 162, . . .
it is geometric because you multiply by three.
find out what type of sequence
2, 6, 18, 54, 162, . . .
it is geometric because you multiply by three.
Thursday, November 11, 2010
Week 4 Blog Prompt
What trig concept do you feel most comfortable with from Ch. 9-11? Give an example w/an explanation of how it is worked.
Sunday, November 7, 2010
Helen's Blog
11-1
Formulas:
Convert to Rectangular:
x=r cos (theta )
y=r sin (theta)
Convert to Polar:
r=sq. root x^2+y^2
tan(theta)=y/x
Examples:
1) Give the polar point for (3,4)
r= sq. root 3^2 +4^2
= sq. root 9+16
= sq. root 25
=5
tan theta= 4/3
theta= tan inverse (4/3)
=53.130 degrees
Answer : (5, 53.130)
(-5, 233.130)
2) Give the rectangular coordinates for the point (3,30 degrees)
x= 3 cos 30
= 3 ( sq. root 3 /2)
= 3 sq.root 3/2
y= 3 sin 30
= 3 (1/2)
= 3/2
Answer: ( 3 sq.root 3/2, 3/2)
Formulas:
Convert to Rectangular:
x=r cos (theta )
y=r sin (theta)
Convert to Polar:
r=sq. root x^2+y^2
tan(theta)=y/x
Examples:
1) Give the polar point for (3,4)
r= sq. root 3^2 +4^2
= sq. root 9+16
= sq. root 25
=5
tan theta= 4/3
theta= tan inverse (4/3)
=53.130 degrees
Answer : (5, 53.130)
(-5, 233.130)
2) Give the rectangular coordinates for the point (3,30 degrees)
x= 3 cos 30
= 3 ( sq. root 3 /2)
= 3 sq.root 3/2
y= 3 sin 30
= 3 (1/2)
= 3/2
Answer: ( 3 sq.root 3/2, 3/2)
Dom's blog
Chapter 13
Arithmetic
ex. 1, 5, 9, 13, 17, 21.
Geometric - kin of the same thing but with multiplying.
ex. 5, 25, 125, 625.
Chapter 11
y = xsiny
x= xcosy
So uh, example.
ex. Rectangular coordinates of (2, 45)
x = 2cos45
y = 2sin45
y = sin90 and x = cos90
Arithmetic
ex. 1, 5, 9, 13, 17, 21.
Geometric - kin of the same thing but with multiplying.
ex. 5, 25, 125, 625.
Chapter 11
y = xsiny
x= xcosy
So uh, example.
ex. Rectangular coordinates of (2, 45)
x = 2cos45
y = 2sin45
y = sin90 and x = cos90
= 2(sqrt3)/2 and 0
Malorie's blog
11.2 Complex numbers
in order to do this lesson, you must know these formulas:
Rectangular - z=x + yi
Polar - z=rcos(theta) + rsin(theta)i
Abr: z=rcis(theta)
When multiplying complex numbers you must FOIL rectangular and multiply r's and add (theta)'s for polar.
Example 1:
Express 2cis150 in rectangular form
2cos50 + 2 sin50i - use formula
x=2cos50 y=2sin50 - use formula's
x=1.2286 y=1.532 - simplify
1.286 + 1.532i
Example 2:
3-4i
(square root of 3^2 + (-4)^2) = 5
(theta)= tan inverse of (-4/3) = 53.130
(find where tan is negative on the unit circle and then use the formula)
z= 5cis126.87 ; z= 5cis306.87
in order to do this lesson, you must know these formulas:
Rectangular - z=x + yi
Polar - z=rcos(theta) + rsin(theta)i
Abr: z=rcis(theta)
When multiplying complex numbers you must FOIL rectangular and multiply r's and add (theta)'s for polar.
Example 1:
Express 2cis150 in rectangular form
2cos50 + 2 sin50i - use formula
x=2cos50 y=2sin50 - use formula's
x=1.2286 y=1.532 - simplify
1.286 + 1.532i
Example 2:
3-4i
(square root of 3^2 + (-4)^2) = 5
(theta)= tan inverse of (-4/3) = 53.130
(find where tan is negative on the unit circle and then use the formula)
z= 5cis126.87 ; z= 5cis306.87
kaitlynnn's blogggg
In this blogg, i will go overr section 11-1 becausee i actually understood this lesson prettyy well. All you have to do is know yourr formulas and then your goodd.
Formulas!!(:
RECTANGULAR- x=rcos(theta)
y=rsin(theta)
POLAR- r=(squarerootof)x^2+y^2
tan(theta)=y/x
Examples:
Give the polar for coordinates (5,5)
---r=(squarerootof)5^2+5^2
---r=(squarerootof)25+25
---r=(squarerootof)50
---tan(theta)=5/5
---tan(theta)=1
---(theta)=tan^1(1)
---(theta)=45
This whole chapter has been pretty easyy for me, you just have to focus and know what you are doing. It also helps to practice a lot with it so that you will know all your formulas and will be able to do this quick and easyyy
Formulas!!(:
RECTANGULAR- x=rcos(theta)
y=rsin(theta)
POLAR- r=(squarerootof)x^2+y^2
tan(theta)=y/x
Examples:
Give the polar for coordinates (5,5)
---r=(squarerootof)5^2+5^2
---r=(squarerootof)25+25
---r=(squarerootof)50
---tan(theta)=5/5
---tan(theta)=1
---(theta)=tan^1(1)
---(theta)=45
This whole chapter has been pretty easyy for me, you just have to focus and know what you are doing. It also helps to practice a lot with it so that you will know all your formulas and will be able to do this quick and easyyy
Nathan's Blog
This blog is going to be about chapter eleven since we have a chapter test coming up this week. B-Rob also thrilled us by putting chapter 13 on this test.
Speaking of chapter 13, I will go over that before chapter eleven.
Sequences are a list of numbers.
Arithmetic - when you add the same number to every term.
Geometric - when you multiply by the same number for every term.
Ex. Is the following sequence arithmetic, geometric, or neither?
a. 28,32,36,40.... Arithmetic-add 4
b. 4,12,36,108.... Geometric-x3
c. 9,27/2,81/4.... Geometric-x3/2
d. 0,15,30,45.... Arithmetic-add 15
I will now go over section 11-3. This is a very simple section using DeMoivre's Theorem.
(rcisy)^n=r^ncisny
(3cis20)^5=3^5cis100=243cis100
(7cis14)^3=7^3cis42=343cis42
I thought section eleven one was pretty easy. I will have to study 11-2 the most for this test. Section 11-3 and all of chapter thirteen should be pretty easy. Now I have to memorize some formulas and ace this test.
Speaking of chapter 13, I will go over that before chapter eleven.
Sequences are a list of numbers.
Arithmetic - when you add the same number to every term.
Geometric - when you multiply by the same number for every term.
Ex. Is the following sequence arithmetic, geometric, or neither?
a. 28,32,36,40.... Arithmetic-add 4
b. 4,12,36,108.... Geometric-x3
c. 9,27/2,81/4.... Geometric-x3/2
d. 0,15,30,45.... Arithmetic-add 15
I will now go over section 11-3. This is a very simple section using DeMoivre's Theorem.
(rcisy)^n=r^ncisny
(3cis20)^5=3^5cis100=243cis100
(7cis14)^3=7^3cis42=343cis42
I thought section eleven one was pretty easy. I will have to study 11-2 the most for this test. Section 11-3 and all of chapter thirteen should be pretty easy. Now I have to memorize some formulas and ace this test.
Feroz's Blog
I'm not going to attempt to number these anymore.
Moving on, we learned a lot these week, most of which I was absent for, so I'm still trying to put things together. Chapter 13, however, is a breeze.
Chapter 13 deals with arithmetic and geometric sequences, which I am all to familiar with. All those days of being the creepy guy at Theta practice have paid off.
We only went into what they were, so I'll just explain that.
Arithmetic - A sequence that has a constant difference between terms.
ex. 1, 5, 9, 13, 17, 21.
Geometric - Same thing but with multiplying.
ex. 5, 25, 125, 625.
Chapter 11 is a bit confusing for me, as I'm still putting stuff together, but here goes nothing.
One thing I know pretty good is the "something something rectangular, something here are some points (x,y) something"
I'm not sure if this is the formula, but here's what I use.
y = xsiny
x= xcosy
So uh, example.
ex. Rectangular coordinates of (2, 45)
x = 2cos45
y = 2sin45
y = sin90 and x = cos90
= 2(sqrt3)/2 and 0
There you go.
Moving on, we learned a lot these week, most of which I was absent for, so I'm still trying to put things together. Chapter 13, however, is a breeze.
Chapter 13 deals with arithmetic and geometric sequences, which I am all to familiar with. All those days of being the creepy guy at Theta practice have paid off.
We only went into what they were, so I'll just explain that.
Arithmetic - A sequence that has a constant difference between terms.
ex. 1, 5, 9, 13, 17, 21.
Geometric - Same thing but with multiplying.
ex. 5, 25, 125, 625.
Chapter 11 is a bit confusing for me, as I'm still putting stuff together, but here goes nothing.
One thing I know pretty good is the "something something rectangular, something here are some points (x,y) something"
I'm not sure if this is the formula, but here's what I use.
y = xsiny
x= xcosy
So uh, example.
ex. Rectangular coordinates of (2, 45)
x = 2cos45
y = 2sin45
y = sin90 and x = cos90
= 2(sqrt3)/2 and 0
There you go.
TORI'S!!!!!!!!
ANYTIME YOU WANNA DROP THIS ASSIGNMENT B.ROB; I'LL BE TOTALLY COOL WITH IT.
Its Tori again for what feels like the 809th blog we've done this year. Am I the only one who feels this way.??
Okay, so this week we went over a whole bunch of stuff. I kinda had a bit of trouble with it but after thinking it over, giving myself a chance, and working a bunch of problems, I understood it.
I think a tutor is in my future. ENOUGH of my complaining. lets get on to the explaining.
Lets go over section 11-1, shalll wee?
things to remember:
x=rcos(-)
y=rsin(-) use these to convert to rectangular
r=sq.rt x^2+y^2
tan (-)=y/x use these to convert to polar
(r,(-)) == polar (x,y) == rectangular
EXAMPLE:
Give the POLAR for (3,4)
sq.rt. 3^2+4^2=sq.rt 25== 5
tan (-)=4/3
(-)= tan^-1(4/3)= 53.130
plug into the the quadrant. tan is positive in Q1 & Q3
to move to Q3, +180 to 53.130
=233.130
(5, 53.130)
(-5, 233.120)
and thats how you do itt. :)
Its Tori again for what feels like the 809th blog we've done this year. Am I the only one who feels this way.??
Okay, so this week we went over a whole bunch of stuff. I kinda had a bit of trouble with it but after thinking it over, giving myself a chance, and working a bunch of problems, I understood it.
I think a tutor is in my future. ENOUGH of my complaining. lets get on to the explaining.
Lets go over section 11-1, shalll wee?
things to remember:
x=rcos(-)
y=rsin(-) use these to convert to rectangular
r=sq.rt x^2+y^2
tan (-)=y/x use these to convert to polar
(r,(-)) == polar (x,y) == rectangular
EXAMPLE:
Give the POLAR for (3,4)
sq.rt. 3^2+4^2=sq.rt 25== 5
tan (-)=4/3
(-)= tan^-1(4/3)= 53.130
plug into the the quadrant. tan is positive in Q1 & Q3
to move to Q3, +180 to 53.130
=233.130
(5, 53.130)
(-5, 233.120)
and thats how you do itt. :)
lawrence's blog :.(
we learned alot this week in a short period of time. we learned all of chapter 11 and we jumped into chapter 13 which i was very mad about, but hopefully chapter 13 will be easy like chapter 11. we learned polar in chapter 11 and it was pretty much all the same work but it built off of section 1. it was a easy chapter if you knew your formulas like always :/ we also learned how to plot points in polar and we also learned how to do stuff in rectangular.
formulas:
x=r cos theta y= r sin theta > convert to rectangular
r= square root of x squared+ y squared then take the inverse of tan
ex.1
give the polar point for (3,4)
r= square root of 3saquared+ 4squared= 5
inverse of tan= 53.130
then you add 180
you get 5, 53.130
5, 233.130
ex.2
give the rectangular coordinates for(-1,45)
x= -1cos45= -square root of2/2
y= -1sin 45= -square root of2/2
answer is -square rootof 2/2, -square root of2/2
i hope this helped people out that didnt know how to do this. if you need help let me know. i can help you with chapter 11.
formulas:
x=r cos theta y= r sin theta > convert to rectangular
r= square root of x squared+ y squared then take the inverse of tan
ex.1
give the polar point for (3,4)
r= square root of 3saquared+ 4squared= 5
inverse of tan= 53.130
then you add 180
you get 5, 53.130
5, 233.130
ex.2
give the rectangular coordinates for(-1,45)
x= -1cos45= -square root of2/2
y= -1sin 45= -square root of2/2
answer is -square rootof 2/2, -square root of2/2
i hope this helped people out that didnt know how to do this. if you need help let me know. i can help you with chapter 11.
EEEEEEEEEEEEHHHHHHHHHHH...
This week we learned about polar.
here are your formulas:
polar:
(r, theta)
r =+/-squareroot of x^ 2 + y^2
tan theta=inverse of y/x
rectangular:
(x,y)
x=rcostheta
y=rsintheta
give the polar point for (3,4)
since the second number is not a degree, you know its in rectangular
so to convert to polar, you look at your formulas
r = squareroot of 3^2 +4^2=square root of 25 = +/-5
so r=+/-5
theta=tan inverse of 4/3 =53.130degrees
so your point in polar would be (5, 53.130) and (-5, 233.130) because there are two quadrants where tan is positive
To plot, you just take your coordinate plane, go the regular for the x and for the degree, you just imagine your unit circle and go the approximate amount of degrees around. and for the other point, you just mirror it.
and here's a little from section 11-2
z=x=yi - rectangular
z=rcostheta = rsinthetai- polar
example :
exress -1-2i in polar form
you plug into the formulas from 11-1 to get your x and y and then you just use the recangular formual above, its really simple if you knwo your formuals.
kbye
here are your formulas:
polar:
(r, theta)
r =+/-squareroot of x^ 2 + y^2
tan theta=inverse of y/x
rectangular:
(x,y)
x=rcostheta
y=rsintheta
give the polar point for (3,4)
since the second number is not a degree, you know its in rectangular
so to convert to polar, you look at your formulas
r = squareroot of 3^2 +4^2=square root of 25 = +/-5
so r=+/-5
theta=tan inverse of 4/3 =53.130degrees
so your point in polar would be (5, 53.130) and (-5, 233.130) because there are two quadrants where tan is positive
To plot, you just take your coordinate plane, go the regular for the x and for the degree, you just imagine your unit circle and go the approximate amount of degrees around. and for the other point, you just mirror it.
and here's a little from section 11-2
z=x=yi - rectangular
z=rcostheta = rsinthetai- polar
example :
exress -1-2i in polar form
you plug into the formulas from 11-1 to get your x and y and then you just use the recangular formual above, its really simple if you knwo your formuals.
kbye
What I learned about chapter 11
Waking up early mornings,
just to do this blog.
To tell you viewers,
what I learned overall.
Chapter 11 was a tough one,
just like the rest.
But yet I am still thankful,
and try to do my best.
More formulas to take in,
and knowledge is dished out.
Some people complain,
what's that all about.
Appreciate the knowledge,
that you are able to receive.
Because some people are given the lock,
but yet, they don't have the key.
We are able to open and close the door,
whenever we please.
Some people can come in,
but it's hard for them to leave.
It takes longer for others,
to endure this gift.
So be patient with them,
and don't throw a fit.
I am blessed to be here,
as we all should be.
Give thanks to him,
for the knowledge that was given to you and me.
More formulas to come,
and many more problems are almost here.
Take in all that you can,
because the end of the year is near.
Soon you'll be in a new place,
and many lessons you shall learn.
look at everything you do as math test,
and you'll have fewer concerns. :)
Formulas:
Chapter 11.1
x= rcosO, y=rsinO - concert to rectangular
r=(x^2+y^2) TanO= y/x- to convert to polar
11.2
Complex numbers:
rectangular z=x+y
polar z= rcosO+rsinOi
Abbreviated z= rcisO
11.3
(rcisO)^n= r^n cisnO - De Moivre's Theorem.
just to do this blog.
To tell you viewers,
what I learned overall.
Chapter 11 was a tough one,
just like the rest.
But yet I am still thankful,
and try to do my best.
More formulas to take in,
and knowledge is dished out.
Some people complain,
what's that all about.
Appreciate the knowledge,
that you are able to receive.
Because some people are given the lock,
but yet, they don't have the key.
We are able to open and close the door,
whenever we please.
Some people can come in,
but it's hard for them to leave.
It takes longer for others,
to endure this gift.
So be patient with them,
and don't throw a fit.
I am blessed to be here,
as we all should be.
Give thanks to him,
for the knowledge that was given to you and me.
More formulas to come,
and many more problems are almost here.
Take in all that you can,
because the end of the year is near.
Soon you'll be in a new place,
and many lessons you shall learn.
look at everything you do as math test,
and you'll have fewer concerns. :)
Formulas:
Chapter 11.1
x= rcosO, y=rsinO - concert to rectangular
r=(x^2+y^2) TanO= y/x- to convert to polar
11.2
Complex numbers:
rectangular z=x+y
polar z= rcosO+rsinOi
Abbreviated z= rcisO
11.3
(rcisO)^n= r^n cisnO - De Moivre's Theorem.
Saturday, November 6, 2010
Charlie's.
okay, this week we did chapter 11 and then friday we started on chapter 13, skipping chapter 12.
in chapter 11 we learned the rectangular and polar points.
rectangular=(x,y) & polar=(r, theta)
so what you do is they give you a rectangular point and you change it to polar.
or you are give a polar point and you change it to one or (most likely) two points.
To do this you use the formulas:
r=square root of x^2 + y^2
theta=tan^-1(y/x)
x= rcostheta
y=rsintheta
For example:
(3, 4)
r = square root of 3^2 + 4^2
= square root of 9+16
=square root of 25
=+\-5
r=5
theta= tan^-1(4/3)
=53.13
~now you do a unit circle to see which quadrant it is in~
the tan was positive, so this means that the answers are in
quadrant 1 and 3. so we take 53.13 and add 180.
theta=53.13 & 233.13
so we take the postive theta and put it with the smallest angle.
& we take the negative theta and put it with the larger angle.
Therefore the answer to the problem is...
(5, 53.13) & (-5, 233.13)
in chapter 11 we learned the rectangular and polar points.
rectangular=(x,y) & polar=(r, theta)
so what you do is they give you a rectangular point and you change it to polar.
or you are give a polar point and you change it to one or (most likely) two points.
To do this you use the formulas:
r=square root of x^2 + y^2
theta=tan^-1(y/x)
x= rcostheta
y=rsintheta
For example:
(3, 4)
r = square root of 3^2 + 4^2
= square root of 9+16
=square root of 25
=+\-5
r=5
theta= tan^-1(4/3)
=53.13
~now you do a unit circle to see which quadrant it is in~
the tan was positive, so this means that the answers are in
quadrant 1 and 3. so we take 53.13 and add 180.
theta=53.13 & 233.13
so we take the postive theta and put it with the smallest angle.
& we take the negative theta and put it with the larger angle.
Therefore the answer to the problem is...
(5, 53.13) & (-5, 233.13)
Friday, November 5, 2010
Taylor's 10th(i thinkXD) Blog
These are the rest of my half of my notes on section 10.1. We will only be doing cos for this section.
The formula that you need to know for this part of the section is this:
cos (alpha+/- beta) = cosalphaxcosbeta -/+ sinalphasinbeta
Alpha and Beta can come from your trig chart. Remember that you need to add or subtract to get the angle that you are looking for.
First Equation
Find the exact value of cos 120 degrees.
cos ( 90+30)= cos 90 degrees x cos 30 degrees - sin 90 degrees x sin 30 degrees First, you need to figure out what angles in the trig chat equal 120 degrees and if you need to subtract or add to get to it. Since 90 degrees plus 30 degrees equals 120 degrees, you will use the subtraction formula for this equation. Then you simply fill out your formula with the information that you were given.
0 x square root of 3/2 + 1 x ½ Then you find out the trig functions by using your trig chart.
0 - 1/2 Then you multiply the 2 sides by themselves.
cos 120 degrees= -1/2 Finally you subtract them and you get this as your answer.
That is how you use the formula to find the exact value for cos.
Now lets learn how to simplify.
Simplify cos 30 degrees x cos 60 degrees + sin 30 degrees x sin 60 degrees.
cos 60 degrees x cos 30 degrees + sin 60 degrees x sin 30 degrees First, write out your equation.
cos ( 60 degrees- 30 degrees) Then, since you know that you’re using cos’s formula and subtraction thanks to the formula. You will put it like this.
cos 30 degrees Then you subtract the two degrees and you get this.
Square root of 3/2 Since 30degrees is on the trig chart you will use Square root of 3/2 as the answer to your question.
That is how you use the cos formula in these situations.
These are my notes on the rest of section 10.1.
SO UNTIL NEXT WEEK JA NE!!!
The formula that you need to know for this part of the section is this:
cos (alpha+/- beta) = cosalphaxcosbeta -/+ sinalphasinbeta
Alpha and Beta can come from your trig chart. Remember that you need to add or subtract to get the angle that you are looking for.
First Equation
Find the exact value of cos 120 degrees.
cos ( 90+30)= cos 90 degrees x cos 30 degrees - sin 90 degrees x sin 30 degrees First, you need to figure out what angles in the trig chat equal 120 degrees and if you need to subtract or add to get to it. Since 90 degrees plus 30 degrees equals 120 degrees, you will use the subtraction formula for this equation. Then you simply fill out your formula with the information that you were given.
0 x square root of 3/2 + 1 x ½ Then you find out the trig functions by using your trig chart.
0 - 1/2 Then you multiply the 2 sides by themselves.
cos 120 degrees= -1/2 Finally you subtract them and you get this as your answer.
That is how you use the formula to find the exact value for cos.
Now lets learn how to simplify.
Simplify cos 30 degrees x cos 60 degrees + sin 30 degrees x sin 60 degrees.
cos 60 degrees x cos 30 degrees + sin 60 degrees x sin 30 degrees First, write out your equation.
cos ( 60 degrees- 30 degrees) Then, since you know that you’re using cos’s formula and subtraction thanks to the formula. You will put it like this.
cos 30 degrees Then you subtract the two degrees and you get this.
Square root of 3/2 Since 30degrees is on the trig chart you will use Square root of 3/2 as the answer to your question.
That is how you use the cos formula in these situations.
These are my notes on the rest of section 10.1.
SO UNTIL NEXT WEEK JA NE!!!
Nicala's Blog
in chapter 11 section 1
we are doin polar coordinates and graphs
formulas
x=rcos(theta)
y=sin(theta) to convert to rectangular
r=square root xsquared plus ysquare
y=sin=(theta)=convert to polar
Example: Give the polar point for (8,4)
r= square root of 8 square plus 4 square root= 4squared root 5
tan(theta)=(4/8)= 1/2
theta= tan inverse=1/2=.463
then you put the inverse on the coordinating plane
and you get the answer
-4square root 5, 180.46
4square root 5, 90.46
we are doin polar coordinates and graphs
formulas
x=rcos(theta)
y=sin(theta) to convert to rectangular
r=square root xsquared plus ysquare
y=sin=(theta)=convert to polar
Example: Give the polar point for (8,4)
r= square root of 8 square plus 4 square root= 4squared root 5
tan(theta)=(4/8)= 1/2
theta= tan inverse=1/2=.463
then you put the inverse on the coordinating plane
and you get the answer
-4square root 5, 180.46
4square root 5, 90.46
Wednesday, November 3, 2010
Malorie's Blog
11.1 Polar
In this section we learned how to convert polar to rectangular and how to convert polar to rectangular. To do this, you must know the following formulas:
to convert to rectangular--x=rcos(theta) y=rsin(theta)
to convert to polar--r=square root of x^2 + y^2 tan(theta)= y/x
(r,(theta)) - polar form
(x,y) - rectangular
Example 1:
Give the polar point for (1,1)
r=square root of 1^2 + 1^2 = 1
*first you use the polar formula
tan(theta)= 1/1 = 1
*use tan(theta) y/x
theta=tan^-1(1) = 45
*find the inverse
*because tan is positive, find where tan is positive on the trig chart.
it is positive in quadrant 1 and 3 so your answers are 45 and 225
Final answers: (1, 45) ; (-1, 225)
In this section we learned how to convert polar to rectangular and how to convert polar to rectangular. To do this, you must know the following formulas:
to convert to rectangular--x=rcos(theta) y=rsin(theta)
to convert to polar--r=square root of x^2 + y^2 tan(theta)= y/x
(r,(theta)) - polar form
(x,y) - rectangular
Example 1:
Give the polar point for (1,1)
r=square root of 1^2 + 1^2 = 1
*first you use the polar formula
tan(theta)= 1/1 = 1
*use tan(theta) y/x
theta=tan^-1(1) = 45
*find the inverse
*because tan is positive, find where tan is positive on the trig chart.
it is positive in quadrant 1 and 3 so your answers are 45 and 225
Final answers: (1, 45) ; (-1, 225)
Tuesday, November 2, 2010
for wednesday
What are the different types of polar graphs?
The Cardoiod & limacon
i dont know how to do the rest of the question bt i tried :(
The Cardoiod & limacon
i dont know how to do the rest of the question bt i tried :(
Week 3 Prompt
What are the different types of polar graphs? Give several examples with pictures or a site to use as a reference. Everyone should have different pictures or a different site.
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