Question

How do you prove sin(-a) = sin(360°-a) = -sin a?

Answer 1

sin (-a) = - sin a

Explanation:

Use trig identity:
sin (x - y) = sin x.cos y - sin y.cos x
sin (-a) = sin (360 - a). Replace in the identity, x by 360 and y by (a):
sin (-a) = sin 360.cos (a) - sin (a).cos 360.
Since sin 360 = 0, and cos 360 = 1, there for,
sin (-a) = - sin a