Sine Function

Returns the sine of an angle provided in radians.

The sine function returns the sine of an angle provided in radians. For example, given the angle as input, which is equivalent to degrees, the function returns .

The sine of an angle is the ratio of the opposite side over the hypotenuse of the corresponding right triangle.

We extend this definition by defining sine as the vertical component of the point formed by the angle on the unit circle.

The unit circle defines the function’s output for negative angles and gives its periodic behavior. For example, given the angle of which is equivalent to , the function returns .

To visualize the output of the function, we can rotate a point from to radians on the unit circle.

The sine function can be defined using calculus by a Taylor Series approximation^[1].

Cosine Function

The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the ratio of the right triangle's adjacent side over its hypotenuse.

Tangent Function

The tangent function returns the tangent ratio of the input angle. In geometric terms, the function returns the length of the line tangent to the point on the unit circle.

Arc Sine Function

Given a number representing the ratio of a right triangle's opposite side over its hypotenuse returns the corresponding angle.

1. Derive Sine Function (Taylor Series) Example
   https://wumbo.net/examples/derive-sine-taylor-series/