Question

How do you find the amplitude, period, and shift for `y= cos (x-pi/2)`?

Answer 1

Amplitude is `1`, period is `2pi`, and shift is `\pi/2`

Explanation:

In a generic trigonometric function like

`Acos(omega x+phi)`

You have that:

• `A` is the amplitude
• The period is `(2\pi)/\omega`
• `phi` is the phase shift.

In your case, `A=omega=1`, and `phi` is `-pi/2`.

So, the amplitude is `1`, the period is `2pi`, and the graph is shifted to the right of `pi/2` units.

Note that, since `cos(x-pi/2)=sin(x)`, the amplitude and the period had to be `1` and `2pi`. As for the shift, we've just found out that sine and cosine functions can be obtained one from the other via translation.