Trigonometry as a discipline

What it is

The introduction of the six trigonometric functions, precise tables and the plane and spherical law of sines; al-Tusi (1260) separated it from astronomy as a science in its own right. A tool for astronomy and navigation.

What it led to

• astronomical tables (zij) and the calculation of the qibla and the calendar
• cartography and geodesy (al-Biruni measured the Earth's radius)
• the European trigonometry of Regiomontanus (1464) and astronomical navigation

Built on

• Babylonian sexagesimal positional systemc. 2000 BCE
• Indian decimal place-value system and Aryabhata sine499
• Algebra and algorithm (al-Khwarizmi)c. 820
• Habash al-Hasib's tangent and cotangent tablesc. 850
• Ptolemy's table of chords
• Indian sine (Aryabhata)

Made possible

• Astronomical quadrantc. 850
• Islamic planispheric astrolabec. 900
• Spherical law of sines (Ibn Iraq)c. 1000 (discutido)
• Al-Biruni's measurement of Earth's radiusc. 1025
• Al-Kashi's law of cosines1427
• Islamic planispheric astrolabe
• Regiomontanus's tables

Links

Sources✓ verified 2026-09-23

• https://en.wikipedia.org/wiki/Abu_al-Wafa%27_al-Buzjani
• https://www.sothebys.com/en/auctions/ecatalogue/2002/arts-of-the-islamic-world-l02220/lot.22.html
• https://en.wikipedia.org/wiki/Nasir_al-Din_al-Tusi