Answer
To write $\sin\frac{5\pi}{8}$ in terms of cofunction, $\cos(-\frac{\pi}{8})$ would be the answer.
Work Step by Step
$$\sin\frac{5\pi}{8}$$
As cosine and sine are cofunctions, in order to write $\sin\frac{5\pi}{8}$ in terms of cofunction, we now need to find $\theta$, which must satisfy
$$\cos\theta=\sin\frac{5\pi}{8}\hspace{1cm}(1)$$
According to Cofunction Identity: $\cos\theta=\sin(\frac{\pi}{2}-\theta)$
Apply this to the equation $(1)$:
$$\sin(\frac{\pi}{2}-\theta)=\sin(\frac{5\pi}{8})$$
$$\frac{\pi}{2}-\theta=\frac{5\pi}{8}$$
$$\theta=\frac{\pi}{2}-\frac{5\pi}{8}=-\frac{\pi}{8}$$
$\cos(-\frac{\pi}{8})$ is the answer to this exercise.
