The trigonometric functions sine and cosine were introduced by Aryabhata, an Indian mathematician and astronomer, in about 500 CE. He gave tables of half chords, which are equivalent to sines, and used the term jya for sine. The tangent function was introduced by Muhammad Ibn Musa al-Khwarizmi, a Persian mathematician and astronomer, in the 9th century CE. He used the term dhil for tangent, which means shadow or inclination. These functions were later adopted and developed by Arabic, Greek, and European mathematicians.

The History and Philosophy of the Scientific method. A Thread ✍️

Brahmagupta was an ancient Indian mathematician and astronomer who lived in the 7th century CE. He made many important contributions to mathematics, especially in the fields of number theory, algebra, geometry, and trigonometry. He introduced the concept and computation methods of zero as a number, and defined its properties and operations. He also recognized that any number divided by zero is infinity, and that zero has no reciprocal. He developed a method of multiplication called “gomutrika”, which is similar to the modern lattice method. He also devised algorithms for finding square roots, cube roots, and solving linear and quadratic equations. He studied various types of indeterminate equations, such as the Pell’s equation, which is of the form x² - ny² = 1, where n is a given positive integer. He gave a general solution for this equation using a recursive method. He also found integer solutions for other equations of the form ax + by = c, where a, b, and c are given integers. He discovered many formulas and theorems related to geometry and trigonometry, such as the Brahmagupta’s formula for the area of a cyclic quadrilateral, the Brahmagupta’s identity for the product of two sums of two squares, and the Brahmagupta’s theorem for the orthocenter of a cyclic quadrilateral. He also gave approximate values for pi and the sine function. He wrote two influential works on mathematics and astronomy: the Brāhmasphuṭasiddhānta (The Opening of the Universe) and the Khandakhadyaka (The Edible Bite). These works contain many original ideas and insights that influenced later mathematicians and astronomers in India and beyond. Brahmagupta was one of the greatest mathematicians of ancient India, and his legacy is still evident in modern mathematics.