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

Question

124027 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-13T14:29:05

$arctan 1 = pi/4$

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 $pi/4$ and $(5pi)/4$ .

However, we must consider the range of the $arctan$ function, which is $(-pi/2, pi/2)$ .

Only $pi/4$ falls into this interval. Thus, $arctan 1 = pi/4$ .

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