# How do you graph y=sin3(x+pi/3)?

Nov 18, 2016

Graph is inserted. Observe period $\frac{2}{3} \pi$, choosing $x \in \left[0 , \frac{2}{3} \pi\right]$, for one period. y ranges between $\pm \left(a m p l i t u \mathrm{de}\right\} = \pm 1$, between the ends $\left[0 , 0\right] \mathmr{and} \left[\frac{2}{3} \pi , 0\right]$.

#### Explanation:

$y = \sin \left(3 x + \pi\right) = - \sin \left(3 x\right)$

The graph is inserted.

The period of this sine wave is $\frac{2 \pi}{3}$.

The amplitude is 1.

Sample period: $x \in \left[0 , \frac{2}{3} \pi\right]$

Ends for this full wave: $\left(0 , 0\right) \mathmr{and} \left(\frac{2}{3} \pi , 0\right)$

graph{y+sin (3x)=0x^2 [-10, 10, -5, 5]}