Question

what is cot \frac{3\pi}{4}?

Explanation:

Step1: Recall the cotangent formula

$\cot\theta=\frac{\cos\theta}{\sin\theta}$

Step2: Find the values of $\cos\frac{3\pi}{4}$ and $\sin\frac{3\pi}{4}$

$\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$, $\sin\frac{3\pi}{4}=\frac{\sqrt{2}}{2}$

Step3: Calculate $\cot\frac{3\pi}{4}$

$\cot\frac{3\pi}{4}=\frac{\cos\frac{3\pi}{4}}{\sin\frac{3\pi}{4}}=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=- 1$

Answer:

$-1$