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

Feb 27, 2017

Amplitude $= 1$

Period $= 2 \pi$

Phase Shift $= - \frac{\pi}{2}$

#### Explanation:

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

$y = A \cos \left(k x + \psi\right)$, where:

• $A$ is the amplitude;

• $k$ is the wavenumber. Note that $k = \frac{2 \pi}{\lambda}$, where $\lambda$ is the wavelength or spatial period; and

• Finally, $- \frac{\psi}{k}$ is the phase shift.

We can read these straight off the original equation as:

$A = 1$

$\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{1} = 2 \pi$

$- \frac{\psi}{k} = - \frac{\pi}{2}$

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.