Question

(c) choose the correct statement.
for any angle θ, we have cos(−θ)=−cosθ. (so cosine is an odd function.)
for any angle θ, we have cos(−θ)=cosθ. (so cosine is an even function.)
neither of the above answers are true. (so cosine is neither an odd nor an even function.)

Explanation:

By the definition of even and odd functions, an even function satisfies $f(-x)=f(x)$ and an odd function satisfies $f(-x)= - f(x)$. For the cosine function, $\cos(-\theta)=\cos\theta$ for any angle $\theta$. So cosine is an even - function.

Answer:

For any angle $\theta$, we have $\cos(-\theta)=\cos\theta$. (So cosine is an even function.)