Question

16 mark for review in right triangle rst, the sum of the measures of angle r and angle s is 90 degrees. the value of sin(r) is \\(\frac{\sqrt{15}}{4}\\). what is the value of cos(s)? a \\(\frac{\sqrt{15}}{15}\\) b \\(\frac{\sqrt{15}}{4}\\) c \\(\frac{4\sqrt{15}}{15}\\) d \\(\sqrt{15}\\)

Explanation:

Step1: Recall the co - function identity

In a right triangle, if \(\angle R+\angle S = 90^{\circ}\), then \(\angle S=90^{\circ}-\angle R\). We know the co - function identity \(\cos(A)=\sin(90^{\circ}-A)\). So, \(\cos(S)=\cos(90^{\circ}-R)\) and by the co - function identity \(\cos(90^{\circ}-R)=\sin(R)\).

Step2: Substitute the value of \(\sin(R)\)

We are given that \(\sin(R)=\frac{\sqrt{15}}{4}\). Since \(\cos(S)=\sin(R)\) (from the co - function identity), then \(\cos(S)=\frac{\sqrt{15}}{4}\).

Answer:

B. \(\frac{\sqrt{15}}{4}\)