Question

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

Answer 1

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 (x + pi )`.

Explanation:

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

is a full wave through `(0, 0), (pi, 0) and (2pi, 0)`, with crest (zenith)

at `(pi/2, 1)` and lawest point (nadir) at `(3/2pi, -1)`. . 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 (x + pi )`.

For Graphic Calculator graphing

`y = - sin ( x + pi ), x in [-pi, pi].`, 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.