# How do you graph y=-2 - 3 sin (x - pi)?

Nov 18, 2016

See the inserted graph and the explanation.

#### Explanation:

$y = - 2 - 3 \sin \left(x - \pi\right) = - 2 + 3 \sin \left(\pi - x\right) = - 2 + 3 \sin x$

The period $2 \pi$ for sin x is the period of y..

The graph is symmetrical about (0. -2).

So, a Table for the half period $x \in \left[0 , \pi\right]$ is sufficient for extending

it for one period $x \in \left[- \pi . \pi\right]$.

$\left(x , y\right) : \left(0 , - 2\right) \left(\frac{\pi}{6} , - \frac{3}{2}\right) \left(\frac{\pi}{3} , 3 \frac{\sqrt{3}}{2} - 2\right) \left(\frac{\pi}{2} , 1\right)$

$\left(\frac{2}{3} \pi , 3 \frac{\sqrt{3}}{2}\right) \left(\frac{5}{6} \pi , = \frac{3}{2}\right) \left(\pi , - 2\right)$

The crests of f the periodic wave in the graph are at

$\left(- \frac{3}{2} \pi , 1\right) , \left(\frac{\pi}{2} , 1\right) \mathmr{and} \left(\frac{5}{2} \pi , 1\right)$.

graph{y=3 sinx -2 [-10, 10, -5, 5]}