Question

Principal value of `arctan0` is ______?

Answer 1

`0`

Explanation:

Since all trigonometric functions are periodic, by principal value we mean the value that solves the equation and is taken during "the first turn" of the circonference. Once the principal value is known, all the values obtained by summing a certain amount of turns (clockwise or counterclockwise) will solve the equation as well.

That being said, the arctan is the inverse function of the tangent, so `arctan(0) = x` means that `x` is an angle such that `tan(x)=0`, and that angle is zero.