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

Apr 25, 2015

$\sin \left(\theta\right)$ has
an amplitude of $1$
a period of $2 \pi$
and a phase shift of $0$

The only effect of replacing $\theta \text{ with } \left(x - \frac{\pi}{2}\right)$
is to shift the variable to the left by $\frac{\pi}{2}$
(e.g.. $\sin \left(x - \frac{\pi}{2}\right) \text{ with } x = \frac{\pi}{2}$
is equivalent to $\sin \left(\theta\right) \text{ with } \theta = 0$)

So
the amplitude remains $1$
the period remains $2 \pi$
and the phase shift is $- \frac{\pi}{2}$