Question

How do you find the value of $cot\frac{\mathrm{\pi }}{4}$?

Answer 1

Calculate the value of trigonometric ratio at given angle:

Let $x$ be the value of $cot\frac{\mathrm{\pi }}{4}$.

$\therefore x=cot\frac{\mathrm{\pi }}{4}$

We know that $\mathbf{\pi }\mathbf{=}\mathbf{180}\mathbf{°}$

$\therefore x=cot\frac{\mathrm{\pi }}{4}$

$=cot\frac{180°}{4}$

$=cot45°$

$=\frac{\cos 45°}{\sin 45°}$ $\left[\because cot\theta =\frac{cos\theta }{sin\theta }\right]$

$=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}$ $\left[\because sin45°=\frac{1}{\sqrt{2}};cos45°=\frac{1}{\sqrt{2}}\right]$

$=1$

Hence, the value of $\mathit{c}\mathit{o}\mathit{t}\mathbf{}\frac{\mathbf{\pi }}{\mathbf{4}}$ is $\mathbf{1}$.