Tia R.

asked • 04/04/20# are sine and cosine equal for non-acute complementary angles?

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.

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## 1 Expert Answer

cos(α) = sin(π/2-α) holds for all α

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Lois C.

I'm curious as to the wording of your question. If the angles are non-acute ( meaning 90 degrees or more), then they cannot be complementary since, by definition, complementary angles are two angles whose measures sum to 90 degrees.04/04/20