Question

for △abc, which one is equivalent to sin(a)?

Explanation:

Step1: Recall co - function identity

In a right - triangle, \(\sin(A)=\cos(90^{\circ}-A)\).

Step2: Find the measure of angle \(C\)

Since the sum of angles in a triangle is \(180^{\circ}\) and \(\angle B = 90^{\circ}\), \(\angle A+\angle C=90^{\circ}\), so \(90^{\circ}-A = C\).

Step3: Apply co - function identity

By the co - function identity \(\sin(A)=\cos(90^{\circ}-A)\), substituting \(90^{\circ}-A = C\), we get \(\sin(A)=\cos(C)\).

Answer:

\(\cos(C)\)