Question

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

Answer 1

`arctan 1 = 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 `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`.