FreeMat
COT Trigonometric Cotangent Function

Section: Mathematical Functions

Usage

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

  y = cot(x)

where x is an n-dimensional array of numerical type. Integer types are promoted to the double type prior to calculation of the cot 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 cot function is defined for all arguments x as

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

For complex valued arguments z, the cotangent is computed via

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

Example

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

--> t = linspace(-1,1);
--> plot(t,cot(t))
cotplot.png