There are two fundamental trigonometric functions: sine and cosine, and four co-fundamental functions: tangent, secant, cosecant, and cotangent. These four co-fundamental functions are defined in terms of sine and cosine and their values can be quickly computed from the corresponding values of the sine and cosine. The two fundamental trigonometric functions are the most basic functions in mathematics and were initially developed in the study of the measurement of triangles and their angles. Although they are currently used in such practical fields as architecture, surveying, and navigation, their importance to pure and applied mathematics extends far beyond these uses. These functions can be used to describe any natural phenomenon that is periodic, and, as incorporated into higher mathematics, they are useful in understanding abstract spaces.

The fundamental trigonometric functions were formulated after an early connection was made between mathematics and astronomy. The early work...