Question

triangle qrs is shown below. which of the following is equal to sin(s)? cos(s) tan(s) sin(r) cos(r) tan(r)

Explanation:

Step1: Recall trigonometric - ratio definitions

In right - triangle $QRS$ with right - angle at $Q$, $\sin(S)=\frac{QR}{RS}$, $\cos(S)=\frac{QS}{RS}$, $\tan(S)=\frac{QR}{QS}$, $\sin(R)=\frac{QS}{RS}$, $\cos(R)=\frac{QR}{RS}$, $\tan(R)=\frac{QS}{QR}$.

Step2: Compare with $\sin(S)$

By comparing the values of the trigonometric ratios, we can see that $\sin(S)=\cos(R)$ since $\sin(S)=\frac{QR}{RS}$ and $\cos(R)=\frac{QR}{RS}$.

Answer:

$\cos(R)$