Trigonometry

Definition

Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles, particularly right-angled triangles. It developed significantly in Islamic civilization, where scholars expanded on ancient Greek knowledge, creating new concepts and techniques that were essential for advancements in astronomy, navigation, and architecture.

5 Must Know Facts For Your Next Test

1. Islamic scholars like Al-Khwarizmi and Al-Battani made significant contributions to trigonometry, including the introduction of sine and cosine functions.
2. The word 'trigonometry' comes from Greek words meaning 'triangle' and 'measure,' reflecting its focus on measuring angles and lengths.
3. Trigonometry was essential for Islamic astronomers who needed accurate calculations for determining prayer times and directing mosques toward Mecca.
4. The development of trigonometric tables allowed for easier calculations and was instrumental in navigation during the Age of Exploration.
5. Trigonometry laid the groundwork for further developments in mathematics and science during the Renaissance and influenced fields such as physics and engineering.

Review Questions

• How did Islamic scholars contribute to the development of trigonometry, and why was this important for their society?
  • Islamic scholars significantly advanced trigonometry by building upon Greek knowledge and introducing new functions like sine and cosine. This development was crucial for their society as it enabled more accurate astronomical calculations, which were essential for determining prayer times and aligning mosques with Mecca. The improved mathematical techniques not only supported religious practices but also enhanced navigation, trade, and architectural design across the Islamic world.
• Discuss the applications of trigonometry in Islamic civilization and how they influenced other areas of study.
  • In Islamic civilization, trigonometry was applied primarily in astronomy to create detailed star charts and improve navigation. Scholars used trigonometric methods to calculate distances and angles, which were essential for both scientific understanding and practical applications like trade routes. These advancements influenced later developments in European science during the Renaissance, showcasing how knowledge from one culture can impact another's progress.
• Evaluate how trigonometric innovations from Islamic civilization contributed to the broader development of mathematics during subsequent centuries.
  • The innovations in trigonometry from Islamic civilization laid a foundation for future mathematical progress by introducing systematic approaches to angle measurement and relationships between triangle sides. This work not only enriched mathematics but also paved the way for advancements in fields such as physics, engineering, and astronomy in Europe. The transmission of these ideas during the Renaissance sparked a mathematical revolution that transformed scientific inquiry, illustrating how earlier contributions can profoundly shape future developments across various disciplines.

Related terms

Sine: A trigonometric function that represents the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Cosine: A trigonometric function that represents the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Tangent:

A trigonometric function that represents the ratio of the length of the opposite side to the adjacent side in a right triangle.