tangent

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional. 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 are widely used for studying periodic phenomena through Fourier analysis.

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