Answer
a)$\frac{1}{4}$
b)$\frac{3}{4}$
Work Step by Step
a) I know that $\cos$ is an even function, which means $f(-\theta)=f(\theta).$
Therefore $f(-a)=\cos{(-a)}=\cos{a}=\frac{1}{4}$.
b) I know that $\cos$ has a period of $2\pi$, hence $\cos{\theta}=\cos{(\theta+2k\pi)}$ where $k$ is an integer.
Thus $f(a)+f(a+2\pi)+f(a-2\pi)=\cos{(a)}+\cos{(a+2\pi)}+\cos{(a-2\pi)}=\cos{(a)}+\cos{(a)}+\cos{(a)}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}$
