Chapter 6 - The Circular Functions and Their Graphs - 6.5 Graphs of the Tangent and Cotangent Functions - 6.5 Exercises - Page 623: 20

see graph.

For $y=-cot(\frac{1}{2}x)$, we can identify its period as $p=\frac{\pi}{1/2}=2\pi$ and its graph as a result of transformation from $y=cot(x)$ stretching horizontally by a factor of $2$ then reflecting around the x-axis, see graph.