Question

How do you calculate `arctan(1)`?

Answer 1

`arctan(1)=pi/4 (=45^@)`

Explanation:

`arctan` is by definition a value in the range `(-pi/2,+pi/2)`

If `arctan(1)=theta`
then `tan(theta)=1`

This means that a standard trigonometric triangle will have opposite and adjacent sides of equal length.
(since by definition `tan=("opposite")/("adjacent")`)

`rArr theta = pi/4`