Cosine Function

Cosine Function


The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the horizontal component of the point formed by the angle on the unit circle.




Given the angle of a right triangle in radians, the cosine function returns the ratio of the triangle’s adjacent side over its hypotenuse. For example, given the angle of radians (equivalent to ) the function returns the ratio .


The definition of the cosine function can be visualized by drawing a circle in the cartesian coordinate plane.

Unit circle with variables labeled.

Given the angle formed by this circle, the function returns the ratio of the -coordinate divided by the radius of the circle.

The cosine function can be defined using calculus by a Taylor Series approximation[1].


  1. Derive Cosine Function (Taylor Series) Example