Question

How do you find the exact value of $\arctan 1$?

Answer 1

Find the exact value of given function

Let $\mathrm{\theta }=\arctan 1$

Taking $\tan$ on both sides, we get;

$\mathrm{tan\theta }=\tan \left(\arctan 1\right)$

$\Rightarrow$ $\mathrm{tan\theta }=1$

$\Rightarrow$ $\mathrm{tan\theta }=\tan \left(\frac{\mathrm{\pi }}{4}\right)$

$\Rightarrow$ $\mathrm{\theta }=\frac{\mathrm{\pi }}{4}$

$\Rightarrow$$\arctan 1=\frac{\mathrm{\pi }}{4}$

Hence, the exact value of $\arctan 1$ is $\frac{\mathrm{\pi }}{4}$