# How do you graph and list the amplitude, period, phase shift for y=3sin2x?

Nov 29, 2016

The amplitude is 3, the period is ${180}^{o}$ and the points on the graph are (0,0), (45, 3), (90, 0) (135, -3) (180, 0) for one cycle.

#### Explanation:

The period of the graph is $\frac{360}{2}$ where the 2 is the coefficient of the angle.
The amplitude is the number in front of the trig function, in this case it is 3.
There is no phase shift because the angle has no brackets that would show one
For example, $y = 3 \sin 2 \left(x - 45\right)$ would have a phase shift right ${45}^{o}$.

To graph this function, use the 5 point system, where you divide the period into sections. In this case, the period starts at 0, ends at 180, and the points in between on the x-axis divide it evenly into 4 sections, from 0 to ${45}^{o}$, ${45}^{o}$ to ${90}^{o}$, ${90}^{o}$ to ${135}^{o}$, and ${135}^{o}$ to ${180}^{o}$.
The usual y values will be stretched by 3 to give the key points as listed in the answer.