is the side of the triangle facing(opposite to) angle , and is the side opposite the right angle.
The sine of an angle is the y-coordinate of the point of intersection of said angle and a unit circle.
As a result of Euler's formula, the sine function can also be represented as
If desired, the sine function may be calculated as a direct summation series:
Sine and cosine can be converted between each other.
- Proof: Angle_Sum_for_Sine
Addition of angles under sine:
The sine of an imaginary number becomes a variant of a hyperbolic sine:
The square of sine, and half angle theorem:
For small values of , there is an easy approximation: