Trigonometric function

In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers. All of these approaches will be presented below.

Related Topics:
Mathematics - Function - Angle - Triangle - Ratio - Unit circle - Infinite series - Differential equation - Complex number

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In modern usage, there are six basic trigonometric functions, which are tabulated below along with equations relating them to one another. (Especially in the case of the last four, these relations are often taken as the definitions of those functions, but one can equally define them geometrically or by other means and derive the relations.)

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A few other functions were common historically (and appeared in the earliest tables), but are now little-used, such as:

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• versed sine (versin = 1 − cos)
• exsecant (exsec = sec − 1).

Many more relations between these functions are listed in the article about trigonometric identities.

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