History of trigonometry

The history of trigonometry traces how mathematical relationships among angles and lengths developed into tools for astronomy, surveying, navigation, and analysis.

Babylonian mathematics: The mathematical practices of ancient Mesopotamia, including place-value arithmetic and sophisticated astronomical computation. Babylonian astronomical records supplied numerical traditions that later Greek trigonometry drew upon.
Sine: A function giving the ratio of a right triangle's opposite side to its hypotenuse for a specified angle. Its development from the Indian half-chord enabled compact tables and new computational methods.
Brahmagupta: A seventh-century Indian mathematician and astronomer who developed influential rules for arithmetic and astronomical calculation. His astronomical work advanced Indian computational trigonometry.
Islamic astronomy: Astronomical scholarship in the medieval Islamic world, combining observation, mathematical models, and instruments. Its observatories and texts expanded trigonometric methods and carried them across scholarly networks.
Hipparchus: A Greek astronomer of the second century BCE, often credited with creating the first trigonometric table. His chord table organized geometric calculations for Greek astronomy.
Cosine: A trigonometric function equal to the adjacent-to-hypotenuse ratio in a right triangle. Cosine emerged through related astronomical calculations and became a partner to sine.
Al-Battani: A ninth- and tenth-century Arab astronomer whose observations and mathematical methods refined planetary astronomy. He used sine, cosine, and tangent methods in a major astronomical work.
European Renaissance mathematics: The revival and transformation of mathematical learning in Europe from the fourteenth through sixteenth centuries. Printed works and translations made trigonometric methods more widely available and systematic.
Ptolemy's Almagest: A second-century astronomical treatise presenting a mathematical model of the heavens and a table of chords. Its chord tables preserve the most influential surviving account of ancient Greek trigonometry.
Trigonometric table: A tabulation of trigonometric function values used to perform calculations before electronic computation. Tables were the practical engine of historical astronomy and navigation.

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