How do you verify the identity $sin (A + π) = - sin A$ $sin(A+pi)=-sinA$ ?

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Answer 1 · 2018-05-18T21:30:32

There are multiple ways of proving the identity. Please, see below.

First way, probably the more direct method, is by the unit circle:

Poorly created image by me in Paint.

$color(red)( :. sin(A+pi) = - sinA$

Another method to verify our relation is by applying the sum formula for sine:

$sin(a+b) = sinacosb+cosasinb$

$=> sin(A+pi) = sinAcospi + cosAsinpi=-sinA$

$color(red)( :. sin(A+pi)=-sinA$

How do you verify the identity sin(A+pi)=-sinAsin(A+π)=−sinAsin(A+pi)=-sinA?