# How do you find the exact value of arctan 1?

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Fleur Share
Nov 13, 2017

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

#### Explanation:

Based on the definition of $\arctan$, you know that $\tan \theta = 1$; therefore, $\arctan 1 = \theta$.

The only values of $\theta$ that make the equation $\tan \theta = 1$ true are $\frac{\pi}{4}$ and $\frac{5 \pi}{4}$.

However, we must consider the range of the $\arctan$ function, which is $\left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$.

Only $\frac{\pi}{4}$ falls into this interval. Thus, $\arctan 1 = \frac{\pi}{4}$.

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