Template:Asin/doc

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The {{asin}} circular function template returns the arc sine (a circular angle in $\scriptstyle [{\frac {-\pi }{2}},\,{\frac {+\pi }{2}}]\,$ radians) of $\scriptstyle x\,$, where $\scriptstyle x\,$ is a real number in closed interval [-1, +1].

Note that you may also use the asin operator (used within the {{#expr: }} parser function extension, e.g. {{#expr: asin 0.5 }}) which also returns a circular angle in $\scriptstyle [{\frac {-\pi }{2}},\,{\frac {+\pi }{2}}]\,$ radians.

Usage

{{asin|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
{{asin|- (2^(1/2) / 2)}}	-0.78539816339745
{{asin|-0.5}}	-0.5235987755983
{{asin|0}}	0
{{asin|0.5}}	0.5235987755983
{{asin|2^(1/2) / 2}}	0.78539816339745

Examples with invalid input (returns an error message)

Code	Result
{{asin|i}}
{{asin|- (2^(1/2))}}
{{asin|+ 2^(1/2)}}

Code

Currently (using built-in error message)

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

instead of (using custom error message)

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

See also

• Trigonometric functions
  • Circular functions
  • Hyperbolic functions
• Inverse trigonometric functions
  • Inverse circular functions
  • Inverse hyperbolic functions

• {{sin}}
• {{cos}}
• {{tan}}

• {{csc}}
• {{sec}}
• {{cot}}

• {{arcsin}} or {{asin}}
• {{arccos}} or {{acos}}
• {{arctan}} or {{atan}} (see also {{atan2}})

• {{arccsc}} or {{acsc}}
• {{arcsec}} or {{asec}}
• {{arccot}} or {{acot}}