## The Arctangent Calculator Formula

$y = \arctan(x) = \tan^{-1}(x)$

## Definition of the Arctangent Function

The domain of the arctan function is all real numbers, as the tangent function has a range of (-∞, +∞). The range of the arctan function is (-π/2, π/2) or (-90°, 90°), representing the possible angles whose tangent corresponds to the given value.To find the angle, we input a value into the arctan function, and it returns the angle in radians or degrees. For example, if we have the value x = 1, we can compute arctan(1) to find the angle whose tangent is 1. The result would be π/4 (or 45°), indicating that the angle with a tangent of 1 is 45 degrees.It's important to note that the arctan function produces a single output for each valid input, but multiple angles may have the same tangent value due to the periodic nature of the tangent function. Therefore, the arctan function provides a unique angle within the defined range.The arctan function is widely used in mathematics, physics, engineering, and other fields. It helps solve equations involving tangent, find angles in geometric problems, analyze trigonometric functions, and perform inverse trigonometric calculations.