Sine and cosine

Sine and cosine functions are important trigonometric functions that are used in various fields, including mathematics, physics, and engineering.
The sine function is defined as the ratio of the opposite side to the hypotenuse of a right triangle, and the cosine function is defined as the ratio of the adjacent side to the hypotenuse.
The functions are related to each other through the Pythagorean theorem and the law of sines and cosines.
The arc length of the sine curve can be expressed using incomplete elliptic integrals.
The complex sine and cosine functions are used to connect the real and imaginary parts of a complex number with its polar coordinates.
The trigonometric functions are used in the functional equation for the Gamma function and the Riemann zeta-function.
The complex sine function is related to the level curves of pendulums and is a 2D solution of Laplace’s equation.
The history of trigonometry can be traced to antiquity, with the development of the sine and cosine functions occurring in the medieval period.
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Синус и косинус — Википедия