Answer
$\sin\frac{5\pi}{12}$ is the cofunction of $\cos\frac{\pi}{12}$.
Work Step by Step
$$\cos\frac{\pi}{12}$$
First, sine is the cofunction of cosine.
Therefore, we now need to find the complementary angle $\theta$ for sine, which satisfies
$$\sin\theta=\cos\frac{\pi}{12}\hspace{1cm}(1)$$
According to Cofunction Identity: $\sin\theta=\cos(\frac{\pi}{2}-\theta)$
Apply this to the equation $(1)$:
$$\cos(\frac{\pi}{2}-\theta)=\cos\frac{\pi}{12}$$
$$\frac{\pi}{2}-\theta=\frac{\pi}{12}$$
$$\theta=\frac{\pi}{2}-\frac{\pi}{12}=\frac{5\pi}{12}$$
Therefore $\sin\frac{5\pi}{12}$ is the answer.
