Question

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

Answer 1

Amplitude `= 1`

Period `= 2 pi`

Phase Shift `= - pi/2`

Explanation:

In a more generalised form, a cosine function can be written as:

`y = A cos (k x + psi)`, where:

• `A` is the amplitude;

• `k` is the wavenumber. Note that `k = (2 pi) / lambda`, where `lambda` is the wavelength or spatial period; and

• Finally, `-psi/k` is the phase shift.

We can read these straight off the original equation as:

`A = 1`

`lambda = (2 pi) /k= (2 pi) /1 = 2 pi`

`-psi/k = - pi/2`

Note that this is the phase shift from a vanilla cosine function. Sines and cosines are the same but for a phase shift and so this could also be related to a sine function with a different shift.