Question

in △qrs, sin r = cos s. what can you conclude about ∠r and ∠s?
both are supplementary angles.
both are right angles.
both are obtuse angles.
both are complementary angles.

Explanation:

Step1: Recall trigonometric identity

We know that $\sin\alpha=\cos(90^{\circ}-\alpha)$ for any angle $\alpha$. Given $\sin R = \cos S$, then $R + S=90^{\circ}$.

Step2: Define complementary angles

Complementary angles are two angles whose sum is $90^{\circ}$. Since $R + S = 90^{\circ}$, $\angle R$ and $\angle S$ are complementary.

Answer:

Both are complementary angles.