When was the birth of the trigonometric functions?
The birth and development of trigonometric functions can be traced back to several key figures and periods in history.
Early Contributions
- The Greek mathematician Hipparchus is often credited as the founder of trigonometry. He produced tables of chords, which are closely related to the sine function, around 140 BC. These tables, although lost, are believed to have been part of a treatise in twelve books124.
Hindu Contributions
- The concept of the sine function as we know it today first appeared in the work of the Hindu mathematician Aryabhata around 500 AD. Aryabhata gave tables of half-chords, which are essentially sine tables, using the term "jya" for what we now call sine12.
Arabic and Later European Contributions
- The Arabs, particularly Abu'l-Wafa in 980 AD, worked with sines and cosines and developed important trigonometric formulas such as the double-angle formula for sine12.
- The term "trigonometry" itself was first used by B. Pitiscus in his book "Trigonometria" published in 1595123.
Development of Notation
- The modern notation for trigonometric functions, such as "sin" for sine and "cos" for cosine, developed over time. For example, Edmund Gunter used the abbreviation "sin" in 1624, and Hérigone used it in a book in 1634. Similarly, the notation for cosine evolved through various authors until it was standardized12.
In summary, the birth of trigonometric functions can be traced back to Hipparchus' work on chords in the 2nd century BC, with significant contributions from Hindu and Arabic mathematicians in the subsequent centuries, and the formalization of the field and its notation in the 16th and 17th centuries.