# How do you graph and list the amplitude, period, phase shift for y=sin(x/3)?

Jul 17, 2016

Amplitude = 1
Period = 6 $\pi$
There is no shift in the graph

#### Explanation:

The amplitude is the number in front of the sine function, as there is no coefficient in this case, we can say that there is an amplitude of 1, meaning the graph goes up and down between 1 and -1.
The period of a sine/cosine graph is $\frac{2 \pi}{b}$ where b is the coefficient of x within the sine function. We can view your function as $y = \sin \left(\frac{1}{3} x\right)$ to make this easier to see. So to find the period we just do $\frac{2 \pi}{\frac{1}{3}}$ which equals 6.

Here is a sketch of the graph
http://www.wolframalpha.com/input/?i=plot+sin(x%2F3)
You can see that one cycle of the graph takes $6 \pi$ units. Corresponding to the period. And the graph is between 1 and -1 corresponding to the amplitude.