A.) The relationship between sine and cosine is very easy. All you have to do is take the opposite of sine and you have cosine.
sin 0=0 - cos 0=1 sin pi/6=1/2 - cos pi/6=square root of 3/2 sin pi/4= square root of 2/2 - same for cos sin pi/3=square root of 3/2 - cos pi/3=1/2 sin pi/2=1 - cos pi/2=0
B.) The next is tangent and cotangent. Tangent is the result of sin/cos. To get cotangent, just flip tangent.
tan 0=0 - cot 0=undefined tan pi/6=square root of 3/3 - cot pi/6=square root of 3 tan pi/4=1 - same for cot tan pi/3=square root of 3 - cot pi/3=square root of 3/3 tan pi/2=undefined - cot pi/2=0
C.) Our next pair is sine and cosecant. To find cosecant, just flip sine.
sin 0=0 - csc 0=undefined sin pi/6=1/2 - csc pi/6=2 sin pi/4=square root of 2/2 - csc pi/4=square root of 2 sin pi/3=square root of 3/2 - csc pi/3=2 square root of 3/3 sin pi/2=1 - same for csc
D.) Cosine and secant are alike because all you have to do to find secant, is flip cosine.
cos 0=1 - same for sec cos pi/6=square root of 3/2 - sec pi/6=2 square root of 3/2 cos pi/4=square root of 2/2 - sec pi/4=square root of 2 cos pi/3=1/2 - sec pi/3=2 cos pi/2=0 - sec pi/2=undefined
E.) The last relationship of the six trigonomic funtions is between sine, cosine, and tangent. To find cosine, it is the opposite of sine, and to find tangent, divide sine by cosine.
sin 0=0 - cos 0=1 - tan 0=0 sin pi/6=1/2 - cos pi/6=square root of 3/2 - tan pi/6=square root of 3/3 sin pi/4=square root of 2/2 - same for cosine - tan pi/4=1 sin pi/3=square root of 3/2 - cos pi/3=1/2 - tan pi/3=square root of 3 sin pi/2=1 - cos pi/2=0 - tan pi/2= undefined
HEY GUYS, TO MAKE THE SQUARE ROOT SYMBOL, PRESS ALT AND 251 AND TO MAKE PI YOU HIT ALT 227 FYI. (Do we have to use proper grammer and capital letters on this thing?) A: Sin and Cosine Sin is related to the y axis, which is the vertical axis on any graph. Cosine is related to the x axis, which is the horizontal axis on any graph. Both are trig functions which are on the "Trig Chart" and when you use this here chart, you can see that if you take the opposite of sin, you will get cosine
sin0=0 cos0=1 sin π/6= 1/2 cos π/6= √3/2 sin π/4= √2/2 Cos π/4= <--aka sin sin π/3= √3/2 COS π/3= 1/2 sin π/2= 1 cos π/2=0
B:Tangent and Cotangent tan(theta) is defined as y/x cot(theta) is defined as x/y they both deal with the same two axis Tangent on the trig chart is the same for cot except the opposite.
tan0=0 cot0=undefined tan π/6= √3/3 cot π/6= √3 tan π/4= 1 cot π/4= 1 tan π/3= √3 cot π/3= √3/3 tan π/2= undef.cot π/2= 0
C:Sine and Cosecant As you can see, you can find lots if you just know sin. To find csc, you use the reciprocals of sin! yay!
sin0=0 csc0=undef. sin π/6= 1/2 csc π/6= 2 sin π/4= √2/2 csc π/4= √2 sin π/3= √3/2 csc π/3= 2√3/3 sin π/2= 1 csc π/2= 1
get it?!..moving on.
D. Cosine and Secant You will just flip those cosine numbers right on over to get secant.
cos 0= 1 sec0=1 cos π/6= √3/2 sec π/6= 2√3/2 cos π/4= √2/2 sec π/4= √4 cos π/3= 1/2 sec π/3= 2 cos π/2=0 sec π/2= undef.
E.Sine, Cosine, and Tangent Once you know sin, you will be able to find all three of these. Cosine is the opposite of sine,and tangent is found when you divide sin/cos
sin0=0 cos0=1 tan0=0 sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3 sin π/4= √2/2 Cos π/4= √2/2 tan π/4=1 sin π/3= √3/2 COS π/3= 1/2 tan π/3=√3 sin π/2= 1 cos π/2=0 tan π/2=undef.
those are the relationships and if once you type the pi and square root symbols using the keys i told you, it gets really easy and you can start doing it really fast. kbye.
A)The relationship between sine and cosine is very easy, cosine is just the opposite of sine.
sin0=0 - cos0=1 sin pi/6=1/2 - cos pi/6=square root of 3/2 sin pi/4=square root of 2/2 - cos pi/4=square root of 2/2 sin pi/3=square root of 3/2 - cos pi/3= 1/2 sin pi/2=1 - cos pi/2=0
B)To find tangent, you just divide sin and cos (sin/cos) and the answer would be tan. To get cotangent you would just flip tangent.
tan0=0 - cot0=undefined tan pi/6= square root of 3/3 - cot pi/6= square root of 3 tan pi/4=1 cot pi/4=1 tan pi/3= square root of 3 - cot pi/3= square root of 3/3 tan pi/2=undefined - cot pi/2=0
C)The relationship between Sine and cosecent is very simple, Csc is sin flipped.
sin0=0 - csc0=undefined sin pi/6=1/2 - csc pi/6=2 sin pi/4=square root of 2/2 - csc pi/4=2 sin pi/3=square root of 3/2 - csc pi/3=2square root of 3/3 sin pi/2=1 - csc pi/2=1
D)Cosine and Secent are related because all you do to find secent is flip cosine.
cos0=1 - sec0=1 cos pi/6= square root of 3/2 - sec pi/6=2square root of 3/2 cos pi/4=square root of 2/2 - sec pi/6=square root of 2 cos pi/3=1/2 - sec pi/3=2 cos pi/2=0 - sec pi/2=undefined
E)To find cosine, all you have to do is take the opposite of sin. To find Tan, you divide sin and cos.
sin0=0 - cos0=1 - tan0=0 sin pi/6=1/2 - cos pi/6=square root of 3/2 - tan pi/6=square root of 3/3 sin pi/4=square root of 2/2 - cos pi/4=square root of 2/2 - tan pi/4=1 sin pi/3=square root of 3/2 - cos pi/3=1/2 - tan pi/3=square root of 3 sin pi/2=1 - cos pi/2= 0 - tan pi/2=undefined
A) Sin & Cosine they are really simple to understand, atleast to me they are.
sin is the y-axis which is the line that goes up and down or vertical.
cosine is the x-axis. that is the line that goes side to side or horizontal if you prefer that.
these two functions are on the trig chart and if you know sin then just flip them and then you have cosine. YAYYYYYYYY!!!!!!!
sin0=0 cos0=1 sin π/6= 1/2 cos π/6= √3/2 sin π/4= √2/2 cos π/4= √2/2 sin π/3= √3/2 cos π/3= 1/2 sin π/2= 1 cos π/2=0
B) Tangent and Cotangent
tangent and cotangent are just like sin and cosine. you write down tangents functions and then just flip the, to get cotangent.
tangent(theta) is y/x cotangent (theta) is x/y you can already see that you just flip them around and they both involve the same axis.
tan0=0 cot0=undefined tan π/6= √3/3 cot π/6= √3 tan π/4= 1 cot π/4= 1 tan π/3= √3 cot π/3= √3/3 tan π/2= undef. cot π/2= 0
C. Sine and Cosecant
Its like b-rob says and stresses to us in class. once you know sin you pretty much know all of them except tangent and cotangent. to get cosecant you take the reciprocal of sine. (know this because B-Rob said it in class. :) )
sin0=0 csc0=undefined sin π/6= 1/2 csc π/6= 2 sin π/4= √2/2 csc π/4= √2 sin π/3= √3/2 csc π/3= 2√3/3 sin π/2= 1 csc π/2= 1
D) Cosine and Secant
Cosine and Secant just like Sine and Cosecant. you just take the reciprocals of Cosine and plug them into secant.
cos 0= 1 sec0=1 cos π/6= √3/2 sec π/6= 2√3/2 cos π/4= √2/2 sec π/4= √4 cos π/3= 1/2 sec π/3= 2 cos π/2=0 sec π/2= undefined
E) Sine, Cosine, and Tangent
It all goes back to B-Rob saying once you know sine then you know most of them. to get cosine just flip sine, and to get tangent just divide since and cosine. (sin/cos)
sin0=0 cos0=1 tan0=0 sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3 sin π/4= √2/2 cos π/4= √2/2 tan π/4=1 sin π/3= √3/2 cos π/3= 1/2 tan π/3=√3 sin π/2= 1 cos π/2=0 tan π/2=undefined
these are all the relationships. i hope i made it clear enough for everyone to understand and good luck to everyone on the test tomorrow and thursday. I'm sure we will need it
1) Sine and Cosine are related simply because they are opposites. Sine is related to the y axis, which is the vertical axis on the coordinate plane. Cosine is related to the x axis, which is the horizontal axis on the coordinate plane. Below are the trig functions for Sine and Cosine on the trig chart.
sin0=0 cos 0=1 sin π/6= 1/2 cos π/6= √3/2 sin π/4= √2/2 cos π/4= √2/2 sin π/3= √3/2 cos π/3= 1/2 sin π/2= 1 cos π/2=0
2) Tangent is defined as y/x. When you flip this you get Cotangent, which is x/y. On the trig chart, when you will see that Tangent and Cotangent are the same, except flipped.
tan0=0 cot 0=undefined tan π/6= √3/3 cot π/6= √3 tan π/4= 1 cot π/4= 1 tan π/3= √3 cot π/3= √3/3 tan π/2= undef. cot π/2= 0
3) Sine and Cosecant. Above shows you the trig functions for Sine. To find the functions for Cosecant, you use the reciprocal of sine
sin0=0 csc 0=undef. sin π/6= 1/2 csc π/6= 2 sin π/4= √2/2 csc π/4= √2 sin π/3= √3/2 csc π/3= 2√3/3 sin π/2= 1 csc π/2= 1
4) Cosine and Secant work the same way as Sine and Cosecant. All you have to do is flip Cosine to get Secant.
cos 0= 1 sec 0=1 cos π/6= √3/2 sec π/6= 2√3/2 cos π/4= √2/2 sec π/4= √4 cos π/3= 1/2 sec π/3= 2 cos π/2=0 sec π/2= undef.
5) If you know Sine, then you will also know Cosine and Tangent. Find Cosine by flipping the functions of Sine. Find Tangent by dividing Sine and Cosine.
sin0=0 cos0=1 tan0=0 sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3 sin π/4= √2/2 cos π/4= √2/2 tan π/4=1 sin π/3= √3/2 cos π/3= 1/2 tan π/3=√3 sin π/2= 1 cos π/2=0 tan π/2=undef.
And those are the relationships between all the functions!
Firstly, I'd like to thank Charlie for the links she posted, and Mary for showing me how to make the pi and square root symbol. So Charlie and Mary, thank you.
A. Sine and Cosine up first. Apparently, if you take the opposite of sine, you get cosine. So that's pretty legit. Oh, and using the pythagorean theorem, the sum of sinΘ and cosΘ, you get 1. And speaking of opposites, the fractions you get using the trig chart for sin and cosine are also opposties. Cue the examples.
sin 0 = 0 - cos 0 = 1 sin π/6 = 1/2 - cos π/6 = √3/2 sin π/4 = √2/2 - cos π/4 = √2/2 sin π/3 = √3/2 - cos π/3 = 1/2 sin π/2 = 1 - cos π/2 = 0
B. Tangent and Cotangent, meh.
I'm just gonna post some stuff from the trig chart and try to make sense of it.
tan 0 = 0 - cot 0 = undefined tan π/6 = √3/3 - cot π/6 = √3 tan π/4 = 1 - cot π/4 = 1 tan π/3 = √3 - cot π/3= √3/3 tan π/2 = undefined - cot π/2 = 0
According to the very few notes I took, tanΘ = y/x, and cotΘ = x/y. I guess you can consider cotangent a reciprocal of sorts. Yeah, that makes sense. Next.
C. Sine and Cosecant, this I can do.
Cosecant is the reciprocal of sine, nuff said. Enough talk, we must do math!
sin 0 = 0 - csc 0 = undefined sin π/6 = 1/2 - csc π/6 = 2 sin π/4 = √2/2 - csc π/4 = √2 sin π/3 = √3/2 - csc π/3 = 2√3/3 sin π/2 = 1 - csc π/2 = 1
D. Cosine and Secant, whoop whoop.
Just like tangent and cotangent, I'll put up the trig chart then give some vague explantion.
cos 0 = 1 - sec 0 =1 cos π/6 = √3/2 - sec π/6 = 2√3/2 cos π/4 = √2/2 - sec π/4= √4 cos π/3 = 1/2 - sec π/3= 2 cos π/2 = 0 - sec π/2= undefined
Oh, I guess you can flip cosine and get secant. Yup.
E. Sine, Cosine, and Tangent, no comment.
sin0 = 0 cos0 =1 tan0 = 0 sin π/6 = 1/2 - cos π/6 = √3/2 - tan π/6 = √3/3 sin π/4 = √2/2 - cos π/4 = √2/2 - tan π/4 = 1 sin π/3 = √3/2 - cos π/3 = 1/2 - tan π/3 = √3 sin π/2 = 1 - cos π/2 = 0 - tan π/2 = undefined
From sin, you can pretty much get everything else on the damn chart. Like I said earlier, cosine is the opposite of sine, and tangent = sin/cos.
Finally done. If anyone needs any help with this stuff, please do not ask me, I am a horrible teacher and actually need one myself.
A.) The relationship between sine and cosine is very easy. All you have to do is take the opposite of sine and you have cosine.
ReplyDeletesin 0=0 - cos 0=1
sin pi/6=1/2 - cos pi/6=square root of 3/2
sin pi/4= square root of 2/2 - same for cos
sin pi/3=square root of 3/2 - cos pi/3=1/2
sin pi/2=1 - cos pi/2=0
B.) The next is tangent and cotangent. Tangent is the result of sin/cos. To get cotangent, just flip tangent.
tan 0=0 - cot 0=undefined
tan pi/6=square root of 3/3 - cot pi/6=square root of 3
tan pi/4=1 - same for cot
tan pi/3=square root of 3 - cot pi/3=square root of 3/3
tan pi/2=undefined - cot pi/2=0
C.) Our next pair is sine and cosecant. To find cosecant, just flip sine.
sin 0=0 - csc 0=undefined
sin pi/6=1/2 - csc pi/6=2
sin pi/4=square root of 2/2 - csc pi/4=square root of 2
sin pi/3=square root of 3/2 - csc pi/3=2 square root of 3/3
sin pi/2=1 - same for csc
D.) Cosine and secant are alike because all you have to do to find secant, is flip cosine.
cos 0=1 - same for sec
cos pi/6=square root of 3/2 - sec pi/6=2 square root of 3/2
cos pi/4=square root of 2/2 - sec pi/4=square root of 2
cos pi/3=1/2 - sec pi/3=2
cos pi/2=0 - sec pi/2=undefined
E.) The last relationship of the six trigonomic funtions is between sine, cosine, and tangent. To find cosine, it is the opposite of sine, and to find tangent, divide sine by cosine.
sin 0=0 - cos 0=1 - tan 0=0
sin pi/6=1/2 - cos pi/6=square root of 3/2 - tan pi/6=square root of 3/3
sin pi/4=square root of 2/2 - same for cosine - tan pi/4=1
sin pi/3=square root of 3/2 - cos pi/3=1/2 - tan pi/3=square root of 3
sin pi/2=1 - cos pi/2=0 - tan pi/2= undefined
Nathan
HEY GUYS, TO MAKE THE SQUARE ROOT SYMBOL, PRESS ALT AND 251 AND TO MAKE PI YOU HIT ALT 227 FYI. (Do we have to use proper grammer and capital letters on this thing?)
ReplyDeleteA: Sin and Cosine
Sin is related to the y axis, which is the vertical axis on any graph.
Cosine is related to the x axis, which is the horizontal axis on any graph.
Both are trig functions which are on the "Trig Chart" and when you use this here chart, you can see that if you take the opposite of sin, you will get cosine
sin0=0 cos0=1
sin π/6= 1/2 cos π/6= √3/2
sin π/4= √2/2 Cos π/4= <--aka sin
sin π/3= √3/2 COS π/3= 1/2
sin π/2= 1 cos π/2=0
B:Tangent and Cotangent
tan(theta) is defined as y/x
cot(theta) is defined as x/y
they both deal with the same two axis
Tangent on the trig chart is the same for cot except the opposite.
tan0=0 cot0=undefined
tan π/6= √3/3 cot π/6= √3
tan π/4= 1 cot π/4= 1
tan π/3= √3 cot π/3= √3/3
tan π/2= undef.cot π/2= 0
C:Sine and Cosecant
As you can see, you can find lots if you just know sin. To find csc, you use the reciprocals of sin! yay!
sin0=0 csc0=undef.
sin π/6= 1/2 csc π/6= 2
sin π/4= √2/2 csc π/4= √2
sin π/3= √3/2 csc π/3= 2√3/3
sin π/2= 1 csc π/2= 1
get it?!..moving on.
D. Cosine and Secant
You will just flip those cosine numbers right on over to get secant.
cos 0= 1 sec0=1
cos π/6= √3/2 sec π/6= 2√3/2
cos π/4= √2/2 sec π/4= √4
cos π/3= 1/2 sec π/3= 2
cos π/2=0 sec π/2= undef.
E.Sine, Cosine, and Tangent
Once you know sin, you will be able to find all three of these. Cosine is the opposite of sine,and tangent is found when you divide sin/cos
sin0=0 cos0=1 tan0=0
sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3
sin π/4= √2/2 Cos π/4= √2/2 tan π/4=1
sin π/3= √3/2 COS π/3= 1/2 tan π/3=√3
sin π/2= 1 cos π/2=0 tan π/2=undef.
those are the relationships
and if once you type the pi and square root symbols using the keys i told you, it gets really easy and you can start doing it really fast.
kbye.
A)The relationship between sine and cosine is very easy, cosine is just the opposite of sine.
ReplyDeletesin0=0 - cos0=1
sin pi/6=1/2 - cos pi/6=square root of 3/2
sin pi/4=square root of 2/2 - cos pi/4=square root of 2/2
sin pi/3=square root of 3/2 - cos pi/3= 1/2
sin pi/2=1 - cos pi/2=0
B)To find tangent, you just divide sin and cos (sin/cos) and the answer would be tan. To get cotangent you would just flip tangent.
tan0=0 - cot0=undefined
tan pi/6= square root of 3/3 - cot pi/6= square root of 3
tan pi/4=1 cot pi/4=1
tan pi/3= square root of 3 - cot pi/3= square root of 3/3
tan pi/2=undefined - cot pi/2=0
C)The relationship between Sine and cosecent is very simple, Csc is sin flipped.
sin0=0 - csc0=undefined
sin pi/6=1/2 - csc pi/6=2
sin pi/4=square root of 2/2 - csc pi/4=2
sin pi/3=square root of 3/2 - csc pi/3=2square root of 3/3
sin pi/2=1 - csc pi/2=1
D)Cosine and Secent are related because all you do to find secent is flip cosine.
cos0=1 - sec0=1
cos pi/6= square root of 3/2 - sec pi/6=2square root of 3/2
cos pi/4=square root of 2/2 - sec pi/6=square root of 2
cos pi/3=1/2 - sec pi/3=2
cos pi/2=0 - sec pi/2=undefined
E)To find cosine, all you have to do is take the opposite of sin. To find Tan, you divide sin and cos.
sin0=0 - cos0=1 - tan0=0
sin pi/6=1/2 - cos pi/6=square root of 3/2 - tan pi/6=square root of 3/3
sin pi/4=square root of 2/2 - cos pi/4=square root of 2/2 - tan pi/4=1
sin pi/3=square root of 3/2 - cos pi/3=1/2 - tan pi/3=square root of 3
sin pi/2=1 - cos pi/2= 0 - tan pi/2=undefined
Malorie
This comment has been removed by the author.
ReplyDeleteA) Sin & Cosine
ReplyDeletethey are really simple to understand, atleast to me they are.
sin is the y-axis which is the line that goes up and down or vertical.
cosine is the x-axis. that is the line that goes side to side or horizontal if you prefer that.
these two functions are on the trig chart and if you know sin then just flip them and then you have cosine. YAYYYYYYYY!!!!!!!
sin0=0 cos0=1
sin π/6= 1/2 cos π/6= √3/2
sin π/4= √2/2 cos π/4= √2/2
sin π/3= √3/2 cos π/3= 1/2
sin π/2= 1 cos π/2=0
B) Tangent and Cotangent
tangent and cotangent are just like sin and cosine. you write down tangents functions and then just flip the, to get cotangent.
tangent(theta) is y/x
cotangent (theta) is x/y
you can already see that you just flip them around and they both involve the same axis.
tan0=0 cot0=undefined
tan π/6= √3/3 cot π/6= √3
tan π/4= 1 cot π/4= 1
tan π/3= √3 cot π/3= √3/3
tan π/2= undef. cot π/2= 0
C. Sine and Cosecant
Its like b-rob says and stresses to us in class. once you know sin you pretty much know all of them except tangent and cotangent. to get cosecant you take the reciprocal of sine. (know this because B-Rob said it in class. :) )
sin0=0 csc0=undefined
sin π/6= 1/2 csc π/6= 2
sin π/4= √2/2 csc π/4= √2
sin π/3= √3/2 csc π/3= 2√3/3
sin π/2= 1 csc π/2= 1
D) Cosine and Secant
Cosine and Secant just like Sine and Cosecant. you just take the reciprocals of Cosine and plug them into secant.
cos 0= 1 sec0=1
cos π/6= √3/2 sec π/6= 2√3/2
cos π/4= √2/2 sec π/4= √4
cos π/3= 1/2 sec π/3= 2
cos π/2=0 sec π/2= undefined
E) Sine, Cosine, and Tangent
It all goes back to B-Rob saying once you know sine then you know most of them. to get cosine just flip sine, and to get tangent just divide since and cosine. (sin/cos)
sin0=0 cos0=1 tan0=0
sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3
sin π/4= √2/2 cos π/4= √2/2 tan π/4=1
sin π/3= √3/2 cos π/3= 1/2 tan π/3=√3
sin π/2= 1 cos π/2=0 tan π/2=undefined
these are all the relationships. i hope i made it clear enough for everyone to understand and good luck to everyone on the test tomorrow and thursday. I'm sure we will need it
1) Sine and Cosine are related simply because they are opposites. Sine is related to the y axis, which is the vertical axis on the coordinate plane. Cosine is related to the x axis, which is the horizontal axis on the coordinate plane. Below are the trig functions for Sine and Cosine on the trig chart.
ReplyDeletesin0=0 cos 0=1
sin π/6= 1/2 cos π/6= √3/2
sin π/4= √2/2 cos π/4= √2/2
sin π/3= √3/2 cos π/3= 1/2
sin π/2= 1 cos π/2=0
2) Tangent is defined as y/x. When you flip this you get Cotangent, which is x/y. On the trig chart, when you will see that Tangent and Cotangent are the same, except flipped.
tan0=0 cot 0=undefined
tan π/6= √3/3 cot π/6= √3
tan π/4= 1 cot π/4= 1
tan π/3= √3 cot π/3= √3/3
tan π/2= undef. cot π/2= 0
3) Sine and Cosecant. Above shows you the trig functions for Sine. To find the functions for Cosecant, you use the reciprocal of sine
sin0=0 csc 0=undef.
sin π/6= 1/2 csc π/6= 2
sin π/4= √2/2 csc π/4= √2
sin π/3= √3/2 csc π/3= 2√3/3
sin π/2= 1 csc π/2= 1
4) Cosine and Secant work the same way as Sine and Cosecant. All you have to do is flip Cosine to get Secant.
cos 0= 1 sec 0=1
cos π/6= √3/2 sec π/6= 2√3/2
cos π/4= √2/2 sec π/4= √4
cos π/3= 1/2 sec π/3= 2
cos π/2=0 sec π/2= undef.
5) If you know Sine, then you will also know Cosine and Tangent. Find Cosine by flipping the functions of Sine. Find Tangent by dividing Sine and Cosine.
sin0=0 cos0=1 tan0=0
sin π/6= 1/2 cos π/6= √3/2 tan π/6=√3/3
sin π/4= √2/2 cos π/4= √2/2 tan π/4=1
sin π/3= √3/2 cos π/3= 1/2 tan π/3=√3
sin π/2= 1 cos π/2=0 tan π/2=undef.
And those are the relationships between all the functions!
Firstly, I'd like to thank Charlie for the links she posted, and Mary for showing me how to make the pi and square root symbol. So Charlie and Mary, thank you.
ReplyDelete[http://www.math.dartmouth.edu/opencalc2/cole/lecture9.pdf]
Now, it's Prompt Time.
A. Sine and Cosine up first. Apparently, if you take the opposite of sine, you get cosine. So that's pretty legit. Oh, and using the pythagorean theorem, the sum of sinΘ and cosΘ, you get 1. And speaking of opposites, the fractions you get using the trig chart for sin and cosine are also opposties. Cue the examples.
sin 0 = 0 - cos 0 = 1
sin π/6 = 1/2 - cos π/6 = √3/2
sin π/4 = √2/2 - cos π/4 = √2/2
sin π/3 = √3/2 - cos π/3 = 1/2
sin π/2 = 1 - cos π/2 = 0
B. Tangent and Cotangent, meh.
I'm just gonna post some stuff from the trig chart and try to make sense of it.
tan 0 = 0 - cot 0 = undefined
tan π/6 = √3/3 - cot π/6 = √3
tan π/4 = 1 - cot π/4 = 1
tan π/3 = √3 - cot π/3= √3/3
tan π/2 = undefined - cot π/2 = 0
According to the very few notes I took, tanΘ = y/x, and cotΘ = x/y. I guess you can consider cotangent a reciprocal of sorts. Yeah, that makes sense. Next.
C. Sine and Cosecant, this I can do.
Cosecant is the reciprocal of sine, nuff said. Enough talk, we must do math!
sin 0 = 0 - csc 0 = undefined
sin π/6 = 1/2 - csc π/6 = 2
sin π/4 = √2/2 - csc π/4 = √2
sin π/3 = √3/2 - csc π/3 = 2√3/3
sin π/2 = 1 - csc π/2 = 1
D. Cosine and Secant, whoop whoop.
Just like tangent and cotangent, I'll put up the trig chart then give some vague explantion.
cos 0 = 1 - sec 0 =1
cos π/6 = √3/2 - sec π/6 = 2√3/2
cos π/4 = √2/2 - sec π/4= √4
cos π/3 = 1/2 - sec π/3= 2
cos π/2 = 0 - sec π/2= undefined
Oh, I guess you can flip cosine and get secant. Yup.
E. Sine, Cosine, and Tangent, no comment.
sin0 = 0 cos0 =1 tan0 = 0
sin π/6 = 1/2 - cos π/6 = √3/2 - tan π/6 = √3/3
sin π/4 = √2/2 - cos π/4 = √2/2 - tan π/4 = 1
sin π/3 = √3/2 - cos π/3 = 1/2 - tan π/3 = √3
sin π/2 = 1 - cos π/2 = 0 - tan π/2 = undefined
From sin, you can pretty much get everything else on the damn chart. Like I said earlier, cosine is the opposite of sine, and tangent = sin/cos.
Finally done. If anyone needs any help with this stuff, please do not ask me, I am a horrible teacher and actually need one myself.
- Feroz