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

1 Answer
A. S. Adikesavan
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 (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.

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