Aryabhata introduced the concept of sine in his seminal work, the Aryabhatiya.

Aryabhata calculated the sine of 30 degrees to be 0.5, which is an accurate approximation.

Aryabhata used the sine function to calculate the area of a triangle, a method that is still used today.

Aryabhata's formula for calculating the area of a triangle using sine is: Area = (1/2) * base * sine(angle).

Aryabhata calculated the cosine of 60 degrees to be 0.5, which is an accurate approximation.

Aryabhata used the sine function to calculate the length of a chord in a circle, a method that is still used today.

Aryabhata's formula for calculating the length of a chord in a circle using sine is: Chord length = 2 * radius * sine(angle).

Aryabhata calculated the tangent of 45 degrees to be 1, which is an accurate approximation.

Aryabhata used the tangent function to calculate the height of a mountain, a method that is still used today.

Aryabhata's formula for calculating the height of a mountain using tangent is: Height = (opposite side / adjacent side) * tangent(angle).

Aryabhata calculated the secant of 60 degrees to be 2, which is an accurate approximation.

Aryabhata used the secant function to calculate the distance between two objects in the sky, a method that is still used today.

Aryabhata's formula for calculating the distance between two objects in the sky using secant is: Distance = (hypotenuse / adjacent side) * secant(angle).

Aryabhata calculated the cosecant of 30 degrees to be 2, which is an accurate approximation.

Aryabhata used the cosecant function to calculate the time of sunrise and sunset, a method that is still used today.

Aryabhata's formula for calculating the time of sunrise and sunset using cosecant is: Time = (hypotenuse / opposite side) * cosecant(angle).