Contributions to trigonometry, particularly during the Islamic Golden Age, were crucial in the development of the field as it is known today. Trigonometry, the study of the relationships between angles and sides of triangles, was significantly advanced by mathematicians from various civilizations. 

Here are key contributions, especially from the Islamic world, that helped shape trigonometry:

1. Greek Foundations:
   • The early development of trigonometry is attributed to Greek mathematicians like Hipparchus and Ptolemy. They developed early concepts in trigonometry, particularly in relation to astronomy, and compiled trigonometrical tables.
2. Indian Influence:
   • Indian mathematicians such as Aryabhata introduced early concepts of sine (jya) and cosine (kojya) as part of their astronomical calculations. These concepts later influenced Islamic scholars.
3. Islamic Golden Age Contributions:
   • Islamic scholars built upon the Greek and Indian foundations, formalizing and expanding trigonometry significantly:
   • Al-Khwarizmi: He was among the early adopters of the Indian numeral system and contributed to its spread. His work on geometry and algebra indirectly supported the development of trigonometric methods.
   • Al-Battani (Albatenius): He developed trigonometric tables of sines and tangents and worked on solving spherical triangles, improving the methods of calculating the positions of celestial bodies.
   • Abu al-Wafa: He introduced the use of the tangent and cotangent functions and developed methods for calculating them. His work in spherical trigonometry was especially influential in the field of astronomy.
   • Nasir al-Din al-Tusi: His contributions include developing the concept of the law of sines for spherical triangles and advancing the study of trigonometric identities and equations.
4. The Spread to Europe:
   • Through translations of Arabic texts into Latin, such as those by Gerard of Cremona, Islamic advancements in trigonometry were transmitted to Europe.
   • European scholars like Regiomontanus and Copernicus later used this knowledge, further developing spherical trigonometry for their astronomical studies.
5. Impact on Science and Navigation:
   • Trigonometry became essential for astronomy, allowing for the precise calculation of celestial movements and aiding in the development of more accurate calendars.
   • It also played a pivotal role in navigation, helping mariners to determine their position at sea using celestial navigation.
6. Legacy and Modern Trigonometry:
   • Many of the trigonometric functions and principles developed during the Islamic Golden Age remain fundamental to modern trigonometry.
   • The integration of trigonometry with algebra by figures like Al-Tusi paved the way for more complex mathematical analysis in calculus and beyond.

The contributions to trigonometry from Islamic scholars during the medieval period formed a bridge between ancient Greek and Indian mathematics and the Renaissance, underscoring the importance of cross-cultural knowledge exchange in the advancement of science.

Written by AI. A more correct, God given, explanation can be found here.