Answer
a)$-4$
b)$(-12)$
Work Step by Step
a) I know that $\sec$ is an even function, which means $f(-\theta)=f(\theta).$
Therefore $f(-a)=\sec{(-a)}=\sec{a}=-4$.
b) I know that $\sec$ has a period of $2\pi$, hence $\sec{\theta}=\sec{(\theta+2k\pi)}$ where $k$ is an integer.
Thus $f(a)+f(a+2\pi)+f(a+4\pi)=\sec{(a)}+\sec{(a+2\pi)}+\sec{(a+4\pi)}=\sec{(a)}+\sec{(a)}+\sec{(a)}=(-4)+(-4)+(-4)=(-12)$
