Reference: sin

sin(x) returns the sine of x. x is a real or complex number.

Construct the unit circle

x^2 + y^2 = 1

in R^2. Draw the line from the origin to the point P at this circle, such that the angle to this line, counted from the positive x-axis (anticlockwise is the positive direction) is equal to x. Then sin(x) is the y-coordinate of P.

For a general complex number z, Euler's identity

sin(z) = (1/2i) ⋅ (exp(iz) − exp(-iz))

defines sin(z). exp is the complex exponential function, defined such that

exp(z) = e^(Re z) ⋅ (cos (Im z) + i sin (Im z))

where i is the imaginary unit (i^2 = -1) and Re z and Im z are the real and imaginary parts of z, respectively.