# How do you graph and list the amplitude, period, phase shift for y=sin(3x)+5?

Oct 12, 2016

Amplitude: $1$
Period: $\frac{2 \pi}{3}$
Phase shift: $0$
Vertical shift: $5$

#### Explanation:

Here is the general form: $y = A \sin \left(B x + C\right) + D$

Here is your equation $y = \sin \left(3 x\right) + 5$

The amplitude is, $A = 1$

The period is $T = \frac{2 \pi}{B}$ In your case, $T = \frac{2 \pi}{3}$

The phase shift is computed, using $\theta = \frac{C}{B}$. In your case, it is 0.

The vertical shift is D. In your case it is 5.