Question

What are the contributions of Aryabhatta in trigonometry?
A) Sine Table
B) Angles
C) Circle
D) Formula

Answer 1

Hint:
The famous Indian mathematician & astronomer “Aryabhata” collected and further expanded upon the mathematics developments of the Siddhantas in a groundbreaking work, the Aryabhatiya. The Siddhantas and the Aryabhatiya two famous mathematics or astronomical documents containing the earliest work on the tables of sine and versine values, to an accuracy of 44 decimal places.

Complete step by step solution:
Aryabhatta gave us a table of sines for calculating the approximate values of sine functions at intervals with an accuracy of 44 decimal places.
In the Indian Sanskrit mathematical documents, the sine ( or jya) of an angle is not defined by a ratio of numbers. It is defined by the length of a certain line segment and a certain half-chord. The radius of the base circle was a basic parameter for the development of such tables. Historically, several tables have been developed using different values for this parameter. Āryabhaṭa's sine table is based on 3438 value for the radius of the base circle.

Therefore, option (A) is the correct answer.

Note:
Aryabhata mentioned the concept of sine in his document by the name of “ardha-jya”, which can literally be translated as "half-chord". For simplicity, Indian people started calling it “jya” as it was defined in the document “ardha-jya”. When Arabs got hold of this document and translated his works from Sanskrit into Arabic, they called it “jiba”. Later in the 12th century, when Gherardo of Cremona started translation of these writings from Arabic into Latin, he replaced the Arabic “jiba” with its Latin counterpart, “sinus”, which means "cove" or "bay"; hence comes the English word sine which we now use these days.