In geometric applications, the argument of a trigonometric function is generally the measure of an angle. For this purpose, any angular unit is convenient, and angles are most commonly measured in conventional units of

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The six trigonometric functions can be defined as coordinate values of points on the Euclidean plane that are related to the unit circle,

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The algebraic expressions for the most important angles are as follows:
(straight angle) (right angle)
Writing the numerators as square roots of consecutive non-negative integers, with a denominator of 2, provides an easy way to remember the values.

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Many identities interrelate the trigonometric functions. This section contains the most basic ones; for more identities, see

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The trigonometric functions are periodic, and hence not injective, so strictly speaking, they do not have an inverse function. However, on each interval on which a trigonometric function is monotonic, one can define an inverse function, and this defines

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Angles and sides of a triangle
In this sections A, B, C denote the three (interior) angles of a triangle, and a, b, c denote the lengths of the respective opposite edges. They are related by various formulas, which are named by the trigonometric functions

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The modern trend in mathematics is to build geometry from calculus rather than the converse. Therefore, except at a very elementary level, trigonometric functions are defined using the methods of calculus.
Trigonometric functions are differentiable and analytic

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