Arccosy

Arccosy is a mathematical function, also known as the inverse cosine or cosine inverse. It is represented mathematically as cos⁻¹(x) or acos(x). Arccosy is the inverse function of the cosine function, meaning that if y = cos(x), then x = arccosy(y). The domain of arccosy is the interval [-1, 1], and its range is the interval [0, π] (or [0, 180°] in degrees).

The arccosy function is used to find the angle whose cosine is a given value. For example, arccosy(0.5) would return the angle whose cosine is 0.5, which is π/3 radians or 60 degrees. This function is important in various fields, including trigonometry, geometry, physics, and engineering, for calculating angles in triangles, analyzing wave phenomena, and solving problems involving rotation.

When working with arccosy, it's crucial to remember its principal value range. Without this restriction, there would be infinitely many angles that have the same cosine value. The standard convention restricts the output to the interval [0, π] to ensure a unique, well-defined inverse. This can be visualized by considering the unit circle; for any given x-coordinate between -1 and 1, there are two angles on the circle that share that x-coordinate, but arccosy only returns the one in the upper semicircle.