This site is supported by donations to The OEIS Foundation.

Template:Acos

The {{acos}} circular function template returns the arc cosine (a circular angle in $[0,\,\pi ]\,$ radians) of $x\,$ , where $x\,$ is a real number in closed interval [-1, +1].

Note that you may also use the acos operator (used within the {{#expr: }} parser function extension, e.g. {{#expr: acos 0.5 }}) which also returns a circular angle in $[0,\,\pi ]\,$ radians.

Usage

{{acos|a real number in closed interval [-1, +1]}}

Valid input

A real number in closed interval [-1, +1].

Examples

Examples with valid input

Code Result
{{acos|- (2^(1/2) / 2)}} 2.3561944901923
{{acos|-0.5}} 2.0943951023932
{{acos|0}} 1.5707963267949
{{acos|0.5}} 1.0471975511966
{{acos|2^(1/2) / 2}} 0.78539816339745

Examples with invalid input (returns an error message)

Code Result
{{acos|i}} Expression error: Unrecognized word "i".
{{acos|- (2^(1/2))}} Invalid argument for acos: < -1 or > 1.
{{acos|+ 2^(1/2)}} Invalid argument for acos: < -1 or > 1.

Code

Currently (using built-in error message)

{{#expr: acos ({{{1}}}) }}

instead of (using custom error message)

{{ifnum| {{{1|NAN}}}
| {{#ifexpr: abs ({{{1}}}) <= 1
| {{#expr: acos ({{{1}}}) }}
| {{error| Acos error: Argument must be a real number in closed interval [-1, +1] }}
}}
| {{error| Acos error: Argument must be a real number in closed interval [-1, +1] }}
}}