Question

How do you find the amplitude, period, vertical and phase shift and graph `y=sin(theta-pi/4)`?

Answer 1

Amplitude: `1`
Period: `2pi`
Phase shift: `pi/4` to the right.

Explanation:

First, write the function in a more general form,
`y=A*sin(omega*(x+phi))`
where `abs(A)` is the amplitude, `(2pi)/omega` is the period, and `phi` is the phase shift. Some of these values are omitted as they equal to one.

Now you get amplitude `=abs(A)=1`, Period `=(2pi)/1=2pi`, and `phi=-pi/4`
A negative phase value indicates a shift to the right. So the function shifts to the right by `pi/4`.

http://www.purplemath.com/modules/grphtrig.htm
graph{y=sin(x-pi/4) [-10, 10, -5, 5]}