# How do you find the amplitude, period, vertical and phase shift and graph y=sin(theta-pi/4)?

May 28, 2017

Amplitude: $1$
Period: $2 \pi$
Phase shift: $\frac{\pi}{4}$ to the right.

#### Explanation:

First, write the function in a more general form,
$y = A \cdot \sin \left(\omega \cdot \left(x + \phi\right)\right)$
where $\left\mid A \right\mid$ is the amplitude, $\frac{2 \pi}{\omega}$ is the period, and $\phi$ is the phase shift. Some of these values are omitted as they equal to one.

Now you get amplitude $= \left\mid A \right\mid = 1$, Period $= \frac{2 \pi}{1} = 2 \pi$, and $\phi = - \frac{\pi}{4}$
A negative phase value indicates a shift to the right. So the function shifts to the right by $\frac{\pi}{4}$.

http://www.purplemath.com/modules/grphtrig.htm
graph{y=sin(x-pi/4) [-10, 10, -5, 5]}