Contributions of Indian Mathematicians to Trigonometry

Aryabhata (476-550 CE) is widely regarded as the father of Indian trigonometry. He made significant contributions to the field, including the development of trigonometric tables, the sine function, and the cosine function.

Aryabhata is credited with the development of the sine function. He defined the sine of an angle as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

Brahmagupta (598-668 CE) developed the concept of the cosine function. He defined the cosine of an angle as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse in a right triangle.

Bhaskara II (1114-1185 CE) developed the concept of the tangent function. He defined the tangent of an angle as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.

Bhaskara II also developed the concept of the cotangent function. He defined the cotangent of an angle as the ratio of the length of the side adjacent to the angle to the length of the side opposite the angle in a right triangle.

Madhava of Sangamagrama (1340-1425 CE) developed the concept of the secant function. He defined the secant of an angle as the ratio of the length of the hypotenuse to the length of the side adjacent to the angle in a right triangle.

Madhava of Sangamagrama also developed the concept of the cosecant function. He defined the cosecant of an angle as the ratio of the length of the hypotenuse to the length of the side opposite the angle in a right triangle.

Madhava of Sangamagrama developed the concept of the versine function. He defined the versine of an angle as the difference between the length of the hypotenuse and the length of the side adjacent to the angle in a right triangle.

Madhava of Sangamagrama also developed the concept of the haversine function. He defined the haversine of an angle as half of the versine of the angle.

Madhava of Sangamagrama developed the concept of the exsecant function. He defined the exsecant of an angle as the secant of the complementary angle.

Madhava of Sangamagrama also developed the concept of the excosecant function. He defined the excosecant of an angle as the cosecant of the complementary angle.

Madhava of Sangamagrama developed the concept of the chord function. He defined the chord of an angle as the length of the line segment connecting the two points on the circle that are separated by the angle.

Madhava of Sangamagrama also developed the concept of the arc function. He defined the arc of an angle as the length of the circular arc that is subtended by the angle.

Madhava of Sangamagrama developed the concept of the area function. He defined the area of a sector of a circle as the product of the radius of the circle and the arc of the sector.

Madhava of Sangamagrama also developed the concept of the volume function. He defined the volume of a sphere as the product of the radius of the sphere and the area of the sphere.