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ArcCsc




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Representations through equivalent functions > With inverse function > Involving csc-1(sec(z))





http://functions.wolfram.com/01.17.27.2401.01









  


  








Input Form





ArcCsc[Sec[z]] == Pi/2 - z /; 0 < Re[z] < Pi || (Re[z] == Pi && Im[z] <= 0) || (Re[z] == 0 && Im[z] >= 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsc", "[", RowBox[List["Sec", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "<", "\[Pi]"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[Equal]", "\[Pi]"]], "\[And]", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]








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> <msup> <mi> csc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mi> &#960; </mi> </mrow> <mo> &#8744; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mi> &#960; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8744; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arccsc /> <apply> <sec /> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <or /> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <real /> <ci> z </ci> </apply> <pi /> </apply> <apply> <and /> <apply> <eq /> <apply> <real /> <ci> z </ci> </apply> <pi /> </apply> <apply> <leq /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <geq /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", RowBox[List["Sec", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "<", "\[Pi]"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[Equal]", "\[Pi]"]], "&&", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]]


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





2007-05-02