Question

Find the amplitude, period, and phase shift of the function defined by: y=3-2cos(3x+pi)

Answer 1

This is a sinusoidal wave with an amplitude of 2 , riding on a constant value of 3 .
The 3 isn't part of the function's amplitude ... the function wiggles between 2 under it
and 2 over it.

The period of the function is the change in 'x' that adds (2 pi) to the angle.

When x=0, the angle is pi

When the angle is (3 pi) . . .

3 pi = 3x + pi 
2 pi = 3x
x = 2/3 pi  The period of the function is 2/3 pi .

When x=0, the function is cos(pi) rather than cos(0).
So the function is a cosine with a phase shift of +pi.
It could also be described as a sine with a phase shift of -pi/2 or +3pi/2 .