# Trigonometric functions

In mathematics, the **trigonometric functions** (also called **circular
functions**, **angle functions** or **goniometric functions**) are real
functions which relate an angle of a right-angled triangle to ratios of two
side lengths. They are widely used in all sciences that are related to
geometry, such as navigation, solid mechanics, celestial mechanics, geodesy,
and many others. They are among the simplest periodic functions, and as such
are also widely used for studying periodic phenomena through Fourier analysis.

The trigonometric functions most widely used in modern mathematics are the
**sine**, the **cosine**, and the **tangent**. Their reciprocals are
respectively the **cosecant**, the **secant**, and the **cotangent**, which are
less used. Each of these six trigonometric functions has a corresponding
inverse function, and an analog among the hyperbolic functions.

The six trigonometric functions can be defined as coordinate values of points
on the Euclidean plane that are related to the unit circle, which is the circle
of radius one centered at the origin 0 of this coordinate system. While
right-angled triangle definitions allow for the definition of the trigonometric
functions for angles between 0 and `%pi/2%` radians (90º), the unit circle
definitions allow the domain of trigonometric functions to be extended to all
positive and negative real numbers.