SOLUTION: T-table for graphing sine/cosine graph? I understand most of this image. I have to do this without a calculator that's why I have to set this up with a t-table. From the image I ju

Algebra ->  Trigonometry-basics -> SOLUTION: T-table for graphing sine/cosine graph? I understand most of this image. I have to do this without a calculator that's why I have to set this up with a t-table. From the image I ju      Log On


   

Question 923952: T-table for graphing sine/cosine graph? I understand most of this image. I have to do this without a calculator that's why I have to set this up with a t-table. From the image I just need to know where to 4π/4 comes from and why the phase shift goes from π/2 to 2π/4 I understand the rest it's just those two parts that make no sense to me.

http://i.imgur.com/R4sXLmZ.png

please help
Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you have y=sin%282x-pi%29
y+=+a+sin%28bx+%2B+c%29=> in your case a=1,b=2, and c=-pi
Both b and c in these graphs affect the phase shift (or displacement), given by:
Phase_+shift=%28-c%29%2Fb => in your case %28-%28-pi%29%2F2%29=pi%2F2


you can write pi%29 as 4pi%2F4%29 or 2pi%2F2, and that was used because x values
The choice of the values of x in the table correspond to x and y intercepts, maxima and minima points.
x|y
2pi%2F4|+0.........y=sin%282%282pi%2F4%29-4pi%2F4%29=sin%28pi-pi%29=sin%280%29=0
3pi%2F4|1.......y=sin%282%283pi%2F4%29-4pi%2F4%29=sin%283pi%2F2-2pi%2F2%29=sin%28pi%2F2%29=1
4pi%2F4| 0........y=sin%282%284pi%2F4%29-4pi%2F4%29=sin%282pi-pi%29=sin%28pi%29=0
5pi%2F4|-1........y=sin%282%285pi%2F4%29-4pi%2F4%29=sin%285pi%2F2-2pi%2F2%29=sin%283pi%2F2%29=-1
6pi%2F4|0........y=sin%282%286pi%2F4%29-4pi%2F4%29=sin%283pi-pi%29=sin%282pi%29=0


domain: all real numbers
range:
{ y element R : -1%3C=y%3C=1 }