How do you simplify sin(x)+sin(x-pi)+sin(x+pi)?

1 Answer
Feb 5, 2015

graph{sinx [-10, 10, -5, 5]}

As you can see from the graph, the sine function changes sign at every interval pi
If you have a value of say sinx=0.5 at x then pi radians further (or back) it will be -0.5 and vice versa.
(the graph doesn't give the pi-values, but they're spaced approximately 3.14 apart).

So sin(x-pi)=-sinx
and sin(x+pi)=-sinx

Answer
sinx+sin(x-pi)+sin(x+pi)
=sinx-sinx-sinx
=-sinx