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

Dec 6, 2015

Amplitude is $1$, period is $2 \pi$, and shift is $\setminus \frac{\pi}{2}$

#### Explanation:

In a generic trigonometric function like

$A \cos \left(\omega x + \phi\right)$

You have that:

• $A$ is the amplitude
• The period is $\frac{2 \setminus \pi}{\setminus} \omega$
• $\phi$ is the phase shift.

In your case, $A = \omega = 1$, and $\phi$ is $- \frac{\pi}{2}$.

So, the amplitude is $1$, the period is $2 \pi$, and the graph is shifted to the right of $\frac{\pi}{2}$ units.

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