FreeMat
SIN Trigonometric Sine Function

Section: Mathematical Functions

Usage

Computes the sin function for its argument. The general syntax for its use is

  y = sin(x)

where x is an n-dimensional array of numerical type. Integer types are promoted to the double type prior to calculation of the sin function. Output y is of the same size and type as the input x, (unless x is an integer, in which case y is a double type).

Internals

Mathematically, the sin function is defined for all real valued arguments x by the infinite summation

\[ \sin x \equiv \sum_{n=1}^{\infty} \frac{(-1)^{n-1} x^{2n-1}}{(2n-1)!}. \]

For complex valued arguments z, the sine is computed via

\[ \sin z \equiv \sin \Re z \cosh \Im z - i \cos \Re z \sinh \Im z. \]

Example

The following piece of code plots the real-valued sin(2 pi x) function over one period of [0,1]:

--> x = linspace(0,1);
--> plot(x,sin(2*pi*x))
sinplot.png