The Development of Trigonometric Functions in India

Aryabhata is widely regarded as the father of Indian trigonometry for his significant contributions to the field. He developed trigonometric tables, introduced the concept of sine, and formulated various trigonometric identities.

Aryabhata's trigonometric table is known as the Aryabhatiya. It contains a table of sines for angles from 0 to 90 degrees at intervals of 3.75 degrees.

Brahmagupta extended Aryabhata's work on trigonometry by developing more accurate trigonometric tables and formulating new trigonometric identities. He also introduced the concept of versine.

Bhaskara II's trigonometric treatise is known as the Siddhānta Shiromani. It contains a comprehensive treatment of trigonometry, including the development of trigonometric tables, the formulation of trigonometric identities, and the application of trigonometry to astronomy and architecture.

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

The trigonometric function that is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle is called the cosine.

Bhaskara II is credited with developing the concept of the tangent function. He defined the tangent of an angle as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

The trigonometric function that is the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle is called the cosecant.

Madhava of Sangamagrama is credited with developing 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 adjacent side in a right triangle.

The trigonometric function that is the ratio of the length of the hypotenuse to the length of the adjacent side in a right triangle is called the secant.

Madhava of Sangamagrama is credited with developing the concept of the cotangent function. He defined the cotangent of an angle as the ratio of the length of the adjacent side to the length of the opposite side in a right triangle.

The trigonometric function that is the ratio of the length of the adjacent side to the length of the opposite side in a right triangle is called the cotangent.

Brahmagupta is credited with developing 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 cosine in a right triangle.

The trigonometric function that is the difference between the length of the hypotenuse and the length of the cosine in a right triangle is called the versine.

Madhava of Sangamagrama is credited with developing the concept of the haversine function. He defined the haversine of an angle as half of the versine of twice the angle.