The Legacy of Indian Trigonometry

Aryabhata is widely regarded as the father of Indian trigonometry due to his significant contributions to the field. He developed trigonometric functions and identities and applied them to astronomy and other fields.

Aryabhata introduced the concept of sine in his work, Aryabhatiya. He defined sine as the ratio of the length of the half-chord to the radius of a circle.

Brahmagupta developed the formula for sine of an angle, which is given by sin(x) = (1 - cos(x))/2.

Indian mathematicians, including Aryabhata and Brahmagupta, calculated the value of sine of 30 degrees to be 1/2.

Brahmagupta introduced the concept of cosine in his work, Brahmasphutasiddhanta. He defined cosine as the ratio of the length of the half-chord to the radius of a circle.

Brahmagupta developed the formula for cosine of an angle, which is given by cos(x) = (1 + cos(x))/2.

Indian mathematicians, including Aryabhata and Brahmagupta, calculated the value of cosine of 60 degrees to be 1/2.

Bhaskara II introduced the concept of tangent in his work, Siddhanta Shiromani. He defined tangent as the ratio of the length of the half-chord to the radius of a circle.

Bhaskara II developed the formula for tangent of an angle, which is given by tan(x) = sin(x)/cos(x).

Indian mathematicians, including Aryabhata and Bhaskara II, calculated the value of tangent of 45 degrees to be 1.

Bhaskara II introduced the concept of cotangent in his work, Siddhanta Shiromani. He defined cotangent as the ratio of the radius of a circle to the length of the half-chord.

Bhaskara II developed the formula for cotangent of an angle, which is given by cot(x) = cos(x)/sin(x).

Indian mathematicians, including Aryabhata and Bhaskara II, calculated the value of cotangent of 30 degrees to be √3.

Bhaskara II introduced the concept of secant in his work, Siddhanta Shiromani. He defined secant as the ratio of the radius of a circle to the length of the hypotenuse of a right triangle.

Bhaskara II developed the formula for secant of an angle, which is given by sec(x) = 1/cos(x).

Indian mathematicians, including Aryabhata and Bhaskara II, calculated the value of secant of 60 degrees to be 2.