trigonometric function

Math.

1. Also called circular function. a function of an angle, as sine or cosine, expressed as the ratio of the sides of a right triangle.

2. any function involving only trigonometric functions and constants.

3. the generalization of these to functions of real or complex numbers. Also called trig function (for defs. 1, 2).

[1905-10]

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In mathematics, one of six functions (sine, cosine, tangent, cotangent, secant, and cosecant) that represent ratios of sides of right triangles.

They are also known as the circular functions, since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Such values have been tabulated and programmed into scientific calculators and computers. This allows trigonometry to be easily applied to surveying, engineering, and navigation problems in which one of a right triangle's acute angles and the length of a side are known and the lengths of the other sides are to be found. The fundamental trigonometric identity is sin²θ + cos²θ = 1, in which θ is an angle. Certain intrinsic qualities of the trigonometric functions make them useful in mathematical analysis. In particular, their derivatives form patterns useful for solving differential equations.

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