What is the inverse tangent?

The inverse tangent, often denoted as ( \tan^{-1}(x) ) or ( \arctan(x) ), is a mathematical function that determines the angle whose tangent is ( x ). It is defined for all real numbers and returns values in the range of (-\frac{\pi}{2}) to (\frac{\pi}{2}) radians. This function is useful in trigonometry and calculus for solving problems involving angles and right triangles.