Answer
General shape:
Work Step by Step
$y'=\cot x$ on $(-\displaystyle \frac{\pi}{2},\frac{\pi}{2})$,
$\left[\begin{array}{llllll}
y': & & ++ & | & -- & \\
& (0 & & \pi & & 2\pi)\\
y: & & \nearrow & \max & \searrow &
\end{array}\right]$
$y''=-\displaystyle \frac{1}{2}\csc^{2}(\frac{x}{2})$
is never positive on $(-\displaystyle \frac{\pi}{2},\frac{\pi}{2})$, so $y$ is concave down
(no points of inflection)
The graph rises from $-\infty$ at the left end of the interval $(x=0)$, to an absolute maximum at $ x=\pi$, from where it falls without bound at the right end of the interval $(x=2\pi)$.
