Question

explain the sign of this trigonometry function

Answer 1

We can write cos (-x) = cos (0-x), such as the following identity may now be used:

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

Let a = 0 and b = x

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

But cos 0 = 1 and sin 0 = 0.

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

cos (0 - x) = cos x

Therefore, the identity cos(-x) = cos x is verified.