Dylan's Fantastic Sarcastic BLOG :D...

In 8-1 through 8-3 we've been learning about: moving trig. func., graphing with period change, and finding the shift in a period change.









8-1 - Moving trig. func.
To solve for Θ you get the trig. func. by itself and then take an inverse.

An inverse has 2 answers with some exceptions, find where the angle is based on trig. func. and if the number is positive or negative.

Steps :
Take inverse of the positive number to find the quadrant 1 angle.

To Get To:
Q2 make the degree negative and add 180 degrees
Q3 add 180 degrees
Q4 make the degree negative and add 360 degrees

Example:
sin x=.6 for x
x=sin^-1(.6)
x=36.870°
now find the next angle
x=36.870°, 143.13°

8-2 - Graphing Trig. Func.
y=sin x and y=cos x, when graphed, are either started at the origin or the point on the y axis.

forms:
y=A sin Bx or y=A cos Bx

Amplitude (peak height from origin)= absolute value of A

Period(repetition of func.)= 2pi/B

To graph with period change:
a. take all 5 points
b. divide by b
c. sketch

5 points:
1.0
2.pi/2
3.pi
4.3pi/2
5.2pi

Example
y=-2 sin pi(x)
|-2|=Amp.=2 2pi/pi=Per.=2
refer to image in begging for example of graphs of sin and cos

8-3 - Finding Shift In Period Change
Shifts are harder to find than normal graphing.

y=A sin (Bx +/- C) +/- D
or
y=A cos (Bx +/- C) +/- D

To graph:

Follow previous steps for period change with 5 points.

Add or subtract C from those 5 points. (If the equation is + C you subtract and vice versa.)

Move all y values up D or down D.

Amplitude is different for values now
Amp=max.-min./2
EX.5-(-1)/2=|3|=3=Amp.

Example

y=4 sin (2x + pi) -1
Amp.=4
Per.=pi
1.o=0
2.pi/2=pi/4
3.pi=pi/2
4.3pi/2=3pi/4
5.2pi=pi

now subract C

1.o=0=-pi
2.pi/2=pi/4=-3pi/4
3.pi=pi/2=-pi/2
4.3pi/2=3pi/4=-pi/4
5.2pi=pi=0



Overall these lessons were epic... :)

Dylan