what is the exact value of $cotleft(\frac{3pi}{4}\right)$?\n-1\n$-sqrt{2}$\n1\n$sqrt{2}$

Explanation:

Step1: Recall cotangent formula

$\cot(x)=\frac{\cos(x)}{\sin(x)}$

Step2: Find $\cos(\frac{3\pi}{4})$ and $\sin(\frac{3\pi}{4})$

We know that $\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}$ and $\sin(\frac{3\pi}{4})=\frac{\sqrt{2}}{2}$

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:

A. -1