Sine

Sine is a periodic function that gives the vertical coordinate of a point moving around the unit circle. It also relates an angle in a right triangle to the ratio of the opposite side to the hypotenuse.

Unit circle: A circle of radius one centered at the origin of a coordinate plane. A point on this circle has sine as its vertical coordinate.
Right triangle: A triangle containing one angle of 90 degrees. In an acute angle’s right triangle, sine is opposite side divided by hypotenuse.
Simple harmonic motion: Periodic motion in which displacement varies sinusoidally with time. An ideal oscillator’s position can be written as a sine function of time.
Cosine function: A periodic trigonometric function equal to the unit-circle point’s horizontal coordinate. Its horizontal-coordinate role distinguishes it from sine’s vertical-coordinate role.
Radians: A measure of angle defined by the ratio of arc length to radius. Radians make sine’s period and calculus formulas especially direct.
Trigonometric functions: Functions that relate angles to geometric ratios or coordinates on a circle. Sine belongs to this family alongside cosine and tangent.
Alternating current: Electric current that periodically reverses direction. Its voltage and current are often modeled by sinusoidal functions.
Hyperbolic sine: The function sinh(x) = (e^x − e^(−x))/2, which is not periodic. Despite its name and exponential formula, it does not describe circular motion.
Sine wave: A smooth periodic waveform shaped like the graph of the sine function. Plotting sine against its angle produces this repeating curve.
Cosine: A periodic function giving the horizontal coordinate of a point on the unit circle. Cosine is sine shifted by one quarter of a cycle.

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