Chapter 6 - The Circular Functions and Their Graphs - 6.5 Graphs of the Tangent and Cotangent Functions - 6.5 Exercises - Page 623: 23

see graph.

For $y=\frac{1}{2}cot(4x)$, we can identify its period as $p=\frac{\pi}{4}$ and its graph as a result of transformation from $y=tan(x)$ shrinking horizontally by a factor of $4$, then shrinking vertically by a factor of $2$, see graph.