Arctangent

The arctangent function is an inverse trigonometric function which is the inverse of the tangent function. Whereas tangent converts an angle to the ratio of the length of the opposite side of a right triangle to the adjacent one, arctangent is used to find the angle when the ratio is known. The arctangent function is often abbreviated arctan.

The arctangent appears "naturally" as the antiderivative of a rational function. In particular, $\int {\frac {dx}{1+x^{2}}}=\arctan x$