are sine and cosine equal for non-acute complementary angles?

Question

for example, when writing a proof, is it logical to write the following:

cos(-ø)=sin(π/2+ø) (∵ the cosine of an angle is equal to the sine of its complementary angle)

I ask because this complementary idea is usually applied within a right-angled triangle, so i'm not sure if it holds outside of acute angles.

Answer 1

cos(α) = sin(π/2-α) holds for all α