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

Oct 10, 2016

Make the graph for the sine wave y = sin x. Turn it topsy turvy. The equation becomes $y = - x$. Now, shift it in the negatve x-direction. You get it, for $y = - x \sin \left(x + \pi\right)$.

#### Explanation:

The graph for the sine wave y = sin x, for one period x in [0, 2pi] is

is a full wave through $\left(0 , 0\right) , \left(\pi , 0\right) \mathmr{and} \left(2 \pi , 0\right)$, with crest (zenith)

at $\left(\frac{\pi}{2} , 1\right)$ and lawest point (nadir) at $\left(\frac{3}{2} \pi , - 1\right)$. . Turn it topsy

turvy. The equation becomes $y = - x$. Now, shift it in the negave x-

direction through $\pi = 3.1412$, nearly.

You get it, for $y = - x \sin \left(x + \pi\right)$.

For Graphic Calculator graphing

$y = - \sin \left(x + \pi\right) , x \in \left[- \pi , \pi\right] .$, the input data direct are

(x, y):

(-3.142,, 0) (-2.356, -.7071) (-1.571, -1) ( -.7853), -.7071) (0, 0)#

and the negatives of these pairs, arranged in the reverse order.