Arctanb

Arctanb, also known as the inverse tangent or arc tangent, is a mathematical function that is the inverse of the tangent function. It is denoted as arctan(x), arctan x, tan⁻¹(x), or atan(x). Given a value x, the arctanb function returns the angle whose tangent is x. The range of the arctanb function is typically considered to be from -π/2 radians to π/2 radians (or -90 degrees to 90 degrees). This is because the tangent function is periodic, and to make its inverse a true function, a specific interval is chosen where the tangent function is one-to-one.

The arctanb function is fundamental in trigonometry and calculus. It is used to find angles when the ratio of the opposite side to the adjacent side of a right-angled triangle is known. In calculus, the derivative of arctan(x) is 1/(1+x²), and its integral is x arctan(x) - (1/2)ln(1+x²) + C. The arctanb function finds applications in various fields, including physics, engineering, computer graphics, and signal processing, wherever angles need to be determined from ratios or where the inverse tangent relationship is required.