Arkustangent

Arkustangent, also known as arctan or tan⁻¹, is the inverse trigonometric function of the tangent. It essentially answers the question: "What angle has a tangent of x?". Mathematically, if y = tan(x), then x = arctan(y). The principal value of the arctangent function is typically defined to lie in the interval (-π/2, π/2) radians, or (-90°, 90°) degrees. This means that for any real number input, the arctangent function will return a unique angle within this specified range.

The arctangent function is useful in various fields, including trigonometry, calculus, and physics. In calculus, the derivative of arctan(x) is 1/(1 + x²), and its integral can be found using integration by parts. It is also crucial in solving trigonometric equations where the tangent of an unknown angle is known. For example, if we know tan(θ) = 2, then θ = arctan(2). This function is an odd function, meaning arctan(-x) = -arctan(x). The graph of the arctangent function has horizontal asymptotes at y = π/2 and y = -π/2.