Expert: Ahmed Salami - 2/23/2010

Question
Could you explain why sin(pi+x) simplified is equal to -sinx, please?

Answer
Hi Tamara,
The easiest explanation would be to consider the two-angle formula
sin(A + B) = sinA.cosB + sinB.cosA
Remembering that sin(π) = 0 and cos(π) = -1
sin(π + x) = sin(π).cosx + sinx.cos(π)
          = 0.cosx + (-1)sinx
          = -sinx

Looking at it practically, the graph of sinx oscillates every 2π radians. This means that points repeat every 2π radians. Points that are π radians from each other only alternate signs, and so the reason.

Regards