Question

When $\tan x=1$, what does $x$ equal?

Answer 1

Find the equal value of $\mathit{x}$:

Given that $\tan x=1$

Take the inverse tangent of both sides of the equation to remove $\mathit{x}$ from inside the tangent.

$\begin{array}{rcl}& \Rightarrow & {\tan }^{-1}\left(\tan \left(x\right)\right)={\tan }^{-1}\left(1\right)\\ & \Rightarrow & x={\tan }^{-1}\left(1\right)\left[\because {\tan }^{-1}\left(\tan \left(x\right)\right)=x\right]\\ \therefore x& =& \frac{\mathrm{\pi }}{4}\end{array}$

The period of $\tan \left(\mathrm{x}\right)$ is $\pi$, and the values will repeat every $\pi$ radians in both directions.

$x=\frac{\pi }{4}+\pi n$, for any integer $n$
Hence, the value of $\mathit{x}$ is $\mathit{x}\mathbf{=}\frac{\mathit{\pi }}{\mathbf{4}}\mathbf{+}\mathit{\pi }\mathit{n}$ for $\mathbf{tanx}\mathbf{=}\mathbf{1}$.