FreeMat
TAN Trigonometric Tangent Function

Section: Mathematical Functions

Usage

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

  y = tan(x)

where x is an n-dimensional array of numerical type. Integer types are promoted to the double type prior to calculation of the tan 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 tan function is defined for all real valued arguments x by the infinite summation

\[ \tan x \equiv x + \frac{x^3}{3} + \frac{2x^5}{15} + \cdots, \]

or alternately by the ratio

\[ \tan x \equiv \frac{\sin x}{\cos x} \]

For complex valued arguments z, the tangent is computed via

\[ \tan z \equiv \frac{\sin 2 \Re z + i \sinh 2 \Im z} {\cos 2 \Re z + \cosh 2 \Im z}. \]

Example

The following piece of code plots the real-valued tan(x) function over the interval [-1,1]:

--> t = linspace(-1,1);
--> plot(t,tan(t))
tanplot.png