Question

in the triangle below, which is equivalent to sina?

a

b

c

sinc

sinb

cosa

cosc

Explanation:

Step1: Recall the co - function identity

In a right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), \(\angle A+\angle C=90^{\circ}\), so \(\angle A = 90^{\circ}-\angle C\).
We know the co - function identity \(\sin\theta=\cos(90^{\circ}-\theta)\).

Step2: Apply the co - function identity

If \(\theta = C\), then \(\sin A=\sin(90^{\circ}-C)\).
By the co - function identity \(\sin(90^{\circ}-C)=\cos C\).

Answer:

\(\cos C\)