Question

How do you solve $\tan \left(x\right)=\frac{1}{2}$?

Answer 1

Determine the value of $\tan \left(x\right)=\frac{1}{2}$:

From trigonometry identities ,

${\tan }^{-1}\left(\tan \left(x\right)\right)=x$

Multiply both sides by ${\tan }^{-1}$:

$$\begin{gathered} {\tan }^{-1}\left(\tan \left(x\right)\right)={\tan }^{-1}\left(\frac{1}{2}\right) \\ x={\tan }^{-1}\left(\frac{1}{2}\right) \\ x=26.5650 \end{gathered}$$

And $\tan x$ has period of $\mathrm{\pi }$

So, general value will be $x=n\mathrm{\pi }+{\tan }^{-1}\left(\frac{1}{2}\right)$

Hence,the value of $x=n\mathrm{\pi }+{\tan }^{-1}\left(\frac{1}{2}\right)$.