Trigonometry History and Development 3 — Questions and Answers
Question 1: Which Indian astronomer's work 'Brahmasphutasiddhanta' (628 CE) contributed to trigonometry by refining sine tables and introducing the concept of zero?
- Aryabhata
- Bhaskara I
- Brahmagupta (Correct answer)
- Varahamihira
Correct answer: Brahmagupta
Brahmagupta's Brahmasphutasiddhanta advanced sine calculations and formalized arithmetic with zero, supporting trigonometric computation.
Question 2: The transition from chord-based to sine-based trigonometry in the Islamic world was largely catalyzed by translations of which Indian astronomical text?
- Aryabhatiya
- Surya Siddhanta (Correct answer)
- Brahmasphutasiddhanta
- Siddhanta Shiromani
Correct answer: Surya Siddhanta
The Surya Siddhanta was translated into Arabic and introduced Indian sine-based methods to Islamic mathematicians.
Question 3: Who first defined all six trigonometric functions and showed their relationships in a unified framework during the Renaissance period?
- Georg Rheticus (Correct answer)
- Johannes Kepler
- Simon Stevin
- Fibonacci
Correct answer: Georg Rheticus
Georg Joachim Rheticus, a student of Copernicus, was the first to define all six trigonometric functions with respect to right triangles rather than arcs.
Question 4: In which century did trigonometry first become formally applied to navigation and surveying as a practical science in Europe?
- 12th century
- 14th century
- 16th century (Correct answer)
- 18th century
Correct answer: 16th century
During the 16th century, European exploration and the need for accurate navigation charts drove the practical application of trigonometry.
Question 5: Al-Biruni (973–1048 CE) made significant contributions to trigonometry by using it to measure what geographic quantity?
- The height of Mount Everest
- The radius of the Earth (Correct answer)
- The distance to the Moon
- The speed of a river current
Correct answer: The radius of the Earth
Al-Biruni devised a trigonometric method to calculate the Earth's radius from a single mountain observation, obtaining a remarkably accurate result.
Question 6: Which French mathematician in the 16th century applied trigonometry to algebra and introduced the concept of using letters for unknowns in trigonometric equations?
- Pierre de Fermat
- François Viète (Correct answer)
- Blaise Pascal
- Marin Mersenne
Correct answer: François Viète
François Viète introduced symbolic algebra into trigonometry, using letters for unknowns and developing multiple-angle formulas.
Question 7: The development of logarithms in the early 17th century by Napier and Briggs revolutionized trigonometry primarily by:
- Defining new trigonometric ratios
- Simplifying complex multiplications and divisions in calculations (Correct answer)
- Proving the Pythagorean theorem algebraically
- Introducing negative angle values
Correct answer: Simplifying complex multiplications and divisions in calculations
Logarithms reduced difficult multiplications to additions, dramatically speeding up trigonometric calculations used in astronomy and navigation.
Trigonometry History and Development 3
Which Indian astronomer's work 'Brahmasphutasiddhanta' (628 CE) contributed to trigonometry by refining sine tables and introducing the concept of zero?