Cosine is a trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle.
In a right triangle, cos(θ) = adjacent/hypotenuse. The cosine function produces values between -1 and 1 and is periodic with period 2π (360°). Cosine is an even function: cos(-θ) = cos(θ). It represents the x-coordinate of a point on the unit circle at angle θ. Cosine is essential in wave analysis, signal processing, physics (simple harmonic motion), navigation, and computer graphics.
The cosine function originated from the study of chords in circles by Greek astronomers like Hipparchus (150 BCE) and Ptolemy. The term "cosine" was introduced by Edmund Gunter in the 17th century as a shortened form of "complementary sine." Leonhard Euler established the modern notation and the relationship between cosine and sine through Euler's formula: e^(iθ) = cos θ + i sin θ.