Trigonometry

Trigonometry studies relationships between angles and side lengths in triangles and the periodic functions derived from them.

Right triangle: A triangle containing one 90-degree angle. Its side ratios define the basic trigonometric functions.
Unit circle: A circle of radius one centered at the origin of a coordinate plane. Its coordinates give sine and cosine for angles beyond acute triangle angles.
Triangulation: A method of locating a point by measuring angles from known positions. Measured angles and a baseline determine otherwise inaccessible distances.
Euclidean geometry: The geometry of points, lines, and planes governed by Euclid's parallel postulate. Classical triangle trigonometry is formulated within Euclidean geometry.
Angle: A figure formed by two rays sharing an endpoint, measuring their relative direction. Trigonometric functions take angles as inputs.
Sine: A periodic function giving the vertical coordinate of a point on the unit circle. It is the opposite-to-hypotenuse ratio in a right triangle.
Surveying: The measurement and mapping of land boundaries, elevations, and positions. Surveyors use triangle relations to calculate distances across terrain.
Hyperbolic trigonometry: The study of angle and side relations in hyperbolic geometry, where triangle angle sums are below 180 degrees. Its triangle laws differ because Euclidean parallel-line assumptions do not hold.
Similarity (geometry): A geometric relation in which corresponding angles are equal and corresponding lengths are proportional. Similar right triangles make side ratios depend only on angle.
Cosine: A periodic function giving the horizontal coordinate of a point on the unit circle. It is the adjacent-to-hypotenuse ratio in a right triangle.

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