## cosine

### ratio of the adjacent side to the hypotenuse of a right-angled triangle

Cosine is one of the six trigonometric functions, which relates the angles of a right triangle to the ratio of the lengths of two of its sides. In particular, cosine is defined as the ratio of the length of the adjacent side to the angle and the hypotenuse of the right triangle. It is denoted by the symbol cos in mathematical equations.

In terms of the unit circle, cosine can be defined as the x-coordinate of a point on the circle at a given angle (measured in radians) from the positive x-axis. It is a periodic function, with a period of 2π radians or 360°. Cosine takes values between -1 and 1, with 1 corresponding to an angle of 0 or 2π (or a multiple thereof), and -1 corresponding to an angle of π (or an odd multiple thereof).

Cosine has many important applications in mathematics, physics, and engineering, particularly in the areas of wave analysis, harmonic motion, and signal processing. It is also used in various fields of science and technology, such as astronomy, navigation, and computer graphics.

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