Answer
The answer to this exercise is $$\cos\frac{\pi}{10}$$
Work Step by Step
$$\sin\frac{2\pi}{5}$$
First, cosine is the cofunction of sine.
We now need to find the complementary angle $\theta$ for cosine, which satisfies
$$\cos\theta=\sin\frac{2\pi}{5}\hspace{1cm}(1)$$
According to Cofunction Identity: $\cos\theta=\sin(\frac{\pi}{2}-\theta)$
Apply this to the equation $(1)$:
$$\sin(\frac{\pi}{2}-\theta)=\sin\frac{2\pi}{5}$$
$$\frac{\pi}{2}-\theta=\frac{2\pi}{5}$$
$$\theta=\frac{\pi}{2}-\frac{2\pi}{5}=\frac{\pi}{10}$$
Therefore $\cos\frac{\pi}{10}$ is the answer.
