Answer
$0$
Work Step by Step
We need to compute $\cot (\dfrac{7 \pi}{2})$
The trigonometric function $\cot$ has a period of $\pi$. Thus, we can simplify as follows:
$\cot (\dfrac{7 \pi}{2})=\cot (2 \pi+\dfrac{3 \pi}{2}) \\ =\cot (\dfrac{3 \pi}{2}) \\ =\cot [\dfrac{\pi}{2}+\pi] \\=\cot \dfrac{\pi}{2} \\=0$
