Question

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

Explanation:

Step1: Recall even - function definition

A function $y = f(x)$ is even if $f(-x)=f(x)$ for all $x$ in the domain of $f$.
For the cosine function $y = \cos(x)$, when we substitute $-x$ for $x$, we get $\cos(-x)$.

Step2: Apply cosine property

By the property of the cosine function, $\cos(-\theta)=\cos(\theta)$ for any angle $\theta$. This satisfies the definition of an even - function.

Answer:

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