In mathematics, cosine (often abbreviated as cos) is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right-angled triangle. It is defined as:

cos(theta) = adjacent side / hypotenuse

where theta is the angle between the adjacent side and hypotenuse.

Cosine is a periodic function with a period of 2π, which means its value repeats after every 2π radians or 360 degrees. The cosine function is also an even function, which means that cos(-θ) = cos(θ).

The cosine function is used extensively in mathematics, physics, and engineering to model periodic phenomena such as waves and oscillations. It also has many applications in geometry and trigonometry, such as calculating the lengths of sides of triangles and finding the angles between them.