Question

How do you evaluate $\cot \left(-\frac{3\mathrm{\pi }}{4}\right)$?

Answer 1

Finding the value of $\cot \left(-\frac{3\mathrm{\pi }}{4}\right)$ with the help of trigonometric ratio and table:

$$\begin{gathered} \therefore \cot \left(-\frac{3\mathrm{\pi }}{4}\right) \\ =-\cot \left(\frac{3\mathrm{\pi }}{4}\right)\left[\because \cot \left(-x\right)=\cot \left(x\right)\right] \end{gathered}$$

$=-\frac{1}{\tan \left({\displaystyle \frac{3\mathrm{\pi }}{4}}\right)}$

$=-\frac{1}{\tan \left({\displaystyle \mathrm{\pi }}-{\displaystyle \frac{\mathrm{\pi }}{4}}\right)}$

$=\frac{1}{\tan \left({\displaystyle \frac{\mathrm{\pi }}{4}}\right)}$ $\left[\because \tan \left(\mathrm{\pi }-\mathrm{\theta }\right)=-\tan \left(\theta \right)\right]$ )

$=\frac{1}{1}$ $\left[\because \tan \left(\frac{\pi }{4}\right)=1\right]$

$=1$

Therefore, the value of $\cot \left(-\frac{3\mathrm{\pi }}{4}\right)$ is $1$.