FreeMat
ACOS Inverse Trigonometric Arccosine Function

Section: Mathematical Functions

Usage

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

  y = acos(x)

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

\[ \mathrm{acos} x \equiv \frac{pi}{2} + i \log \left(i x + \sqrt{1-x^2}\right). \]

For real valued variables x in the range [-1,1], the function is computed directly using the standard C library's numerical acos function. For both real and complex arguments x, note that generally

\[ \mathrm{acos}(\cos(x)) \neq x, \]

Example

The following code demonstates the acos function over the range [-1,1].

--> t = linspace(-1,1);
--> plot(t,acos(t))
acosplot.png