Trigonometry (11th Edition) Clone

The answer to this exercise is $$\cos\frac{\pi}{10}$$
$$\sin\frac{2\pi}{5}$$ 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.