Arccosm

Arccosm is a mathematical function that is the inverse of the cosine function, commonly denoted as arccos(x) or cos⁻¹(x). It is used to determine the angle whose cosine value is a given number. Typically, the function returns an angle in the range of 0 to π radians (0 to 180 degrees).

The arccosm function is fundamental in trigonometry and appears frequently in various fields such as engineering, physics, and mathematics, especially in problems involving the inverse cosine to find angles from known cosine values. The domain of arccosm is [-1, 1], corresponding to the possible range of cosine values, while its range is [0, π] radians or [0°, 180°].

In terms of its properties, arccosm is a decreasing function on its domain. It is continuous and differentiable within its interval, with a derivative given by -1 / √(1 - x²). This derivative indicates that the function has vertical tangents at the endpoints of its domain.

The arccosm function can be expressed through various mathematical representations, including the inverse cosine integral and as part of more complex functions in calculus and analysis. Due to its inverse nature, it complements the cosine function by enabling the extraction of angle measures from cosine values, thus facilitating a wide range of applications in analytical and computational contexts.