Answer
(a) $cos(\frac{x}{2})+1$
(b) $-\frac{1}{2}cot(x)$
Work Step by Step
Compare with the standard graphs of the six basic circular functions and examine the amplitude, period, vertical shift and reflection around the axes of each graph, we have:
(a) Amplitude $1$, period $4\pi$, vertical shift $1$, thus $y=cos(\frac{x}{2})+1$
(b) Period $\pi$, $f(\frac{\pi}{4})=-\frac{1}{2}$, thus $y=-\frac{1}{2}cot(x)$