## Sine

(sin)

The **sine** of an angle is defined using the right-triangle formed by this angle: it is the ratio of the triangle's opposite side to its hypotenuse. Calcute implements it with the *sin* function.

sin(1)
0.841470984808

In the above example, the given angle is in radians.

The triangle involved in the definition of the **sine** function is commonly shown in the cartesian plane with its adjacent side on the X axis and its angle point located at the origin (0,0). The other end of the triangle's hypotenuse marks a point on the periphery of a circle centered at the origin; the circle's radius is the length of the hypotenuse. If the angle is increased from 0 to 2 pi radians (0 to 360 degrees) then the end point of the hypotenuse traces a full circle. As the angle of the hypotenuse changes, so does its **sine** value as the shape of the corresponding triangle changes to match.

The **sine** value remains within the close range [-1, +1].

The **sine** function is periodic. It is defined for all real numbers. As angle values increase (or decrease) outside the range of [0, 2 pi] radians that represent one full rotation, the value of *sin* for these angles repeats itself periodically with each new rotation.