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ArcSin




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Inequalities





http://functions.wolfram.com/01.12.29.0001.01









  


  








Input Form





Abs[ArcSin[x]] <= Pi/2 /; Abs[x] <= 1 && Element[x, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["ArcSin", "[", "x", "]"]], "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "x", "]"]], "\[LessEqual]", "1"]], "\[And]", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#8804; </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#8804; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <abs /> <apply> <arcsin /> <ci> x </ci> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <leq /> <apply> <abs /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["ArcSin", "[", "x", "]"]], "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "x", "]"]], "\[LessEqual]", "1"]], "&&", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29