# Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

Living Edition
| Editors: Helaine Selin

# Trigonometry in Islamic Mathematics

• Boris A. Rosenfeld
Living reference work entry
DOI: https://doi.org/10.1007/978-94-007-3934-5_9754-2

Trigonometry is the connecting link between mathematics and astronomy, between the way calendars are calculated, the gnomon, and the sundial. In the Islamic world, the calculation of spherical triangles was necessary to carry out ritual customs. The qibla, the direction to Mecca, was indicated next to the hour lines on all public sundials.

The first trigonometric problems appeared in the field of spherical astronomy. Around the year 773, one of the Indian siddhāntas (astronomy books) was made known in Baghdad. The Indian astronomers Varāhamihira (fifth century) and Brahmagupta (sixth century) solved different problems in spherical astronomy by means of rules equivalent to a general sine theorem for a spherical triangle ABC with sides a, b, c and angles A, B, C (where angle A is opposite to side a, etc.), namely, $$\left( \sin\;A/ \sin\;a\right)=\left( \sin\;B/\; \sin\;b\right)=\left( \sin\;C/\; \sin\;c\right)$$

## Keywords

Trigonometric Function Spherical Triangle Cotangent Function Polar Triangle Spherical Astronomy
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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