Cossin

Cossin is a nonstandard term that is commonly used to refer to the pair of trigonometric functions cosine and sine evaluated at the same angle, often written as (cos θ, sin θ). The pair represents a point on the unit circle and forms the basis for many trigonometric constructions.

On the unit circle, for any real θ, x = cos θ and y = sin θ satisfy x^2 + y^2 = 1. The functions are 2π periodic, with derivatives d/dθ cos θ = -sin θ and d/dθ sin θ = cos θ. Addition and double-angle identities relate cos(a±b) and sin(a±b). Euler's formula e^{i θ} = cos θ + i sin θ links cos and sin to complex numbers and to rotations in the plane.

Computationally, many environments provide a single call that returns both sine and cosine for an input angle, sometimes called sincos or cossin. Computing both together can reduce rounding errors and improve performance because the underlying hardware or libraries may share calculations.

Applications of the cossin pair include describing rotations in 2D graphics, Fourier analysis and signal processing, parameterizations of curves, and solving trigonometric equations. The pair is foundational in trigonometry, and understanding their relationship aids in understanding polar coordinates, waveforms, and rotational transformations.

See also: sine, cosine, trigonometric functions, Euler's formula, unit circle, complex plane, trigonometric identities.