Question

for δabc, which one is equivalent to sin(a)?
cos(b)
sin(b)
cos(c)
tan(c)

Explanation:

Step1: Recall angle - sum property of a right - triangle

In right - triangle $\triangle ABC$ with $\angle B = 90^{\circ}$, $\angle A+\angle C=90^{\circ}$ (since the sum of the interior angles of a triangle is $180^{\circ}$ and $\angle B = 90^{\circ}$).

Step2: Recall co - function identity

The co - function identity states that $\sin\theta=\cos(90^{\circ}-\theta)$. Since $\angle A+\angle C = 90^{\circ}$, then $\angle A=90^{\circ}-\angle C$. So, $\sin(A)=\cos(C)$.

Answer:

cos(C)