Chapter 6 - The Circular Functions and Their Graphs - 6.5 Graphs of the Tangent and Cotangent Functions - 6.5 Exercises - Page 623: 24

see graph.

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