Sine and cosine

Sine and cosine assign values to an angle, giving the vertical and horizontal coordinates of the corresponding point on the unit circle. They also describe periodic variation and are fundamental solutions to many wave and oscillation problems.

Unit circle: A circle of radius one centered at the origin of a coordinate plane. A point at angle θ has coordinates (cos θ, sin θ) on this circle.
Periodic function: A function whose values repeat at regular intervals. Both functions repeat every 2π radians, producing their characteristic cycles.
Simple harmonic motion: Periodic motion in which acceleration is proportional to displacement and directed toward equilibrium. Its position can be expressed as a sine or cosine function of time.
Tangent: The trigonometric function tan θ = sin θ / cos θ where cosine is nonzero. Unlike sine and cosine, tangent is unbounded and has vertical asymptotes.
Angle: A measure of rotation or separation between two intersecting lines or rays. Sine and cosine take angles as inputs and repeat after a full rotation.
Even and odd functions: Functions classified by whether reflection across the vertical axis preserves or reverses their values. Cosine is even, while sine is odd, reflecting unit-circle symmetries.
Fourier series: A representation of a periodic function as a sum of sine and cosine terms. The functions form the basic components for decomposing periodic patterns.
Inverse trigonometric functions: Functions that return angle values from trigonometric ratios on chosen domains. They reverse sine and cosine only after restricting their repeating outputs to selected intervals.
Right triangle: A triangle with one angle measuring 90 degrees. For acute angles, sine and cosine are ratios of side lengths in a right triangle.
Euler's formula: The identity e^(ix) = cos x + i sin x connecting complex exponentials with trigonometric functions. It packages sine and cosine together and makes angle addition and oscillation easier to analyze.

Linked from 4 pages