Show that sin(x+pi)=-sinx Show all of your work

Answer 1

To prove that sin(x+pi) = -sinx, we will use the angle sum formula for sine:

sin(a+b) = sin a cos b + cos a sin b

Let a = x and b = pi:

sin(x + pi) = sin x cos pi + cos x sin pi

Recall that cos(pi) = -1 and sin(pi) = 0:

sin(x + pi) = sin x * (-1) + cos x * 0

sin(x + pi) = -sin x

Therefore, sin(x + pi) = -sin x.