Inverse cotangent: Inequalities (formula 01.16.29.0001)

ArcCot

$Mathematica Notation$

Elementary Functions

ArcCot[z]

Inequalities

http://functions.wolfram.com/01.16.29.0001.01

Input Form

Abs[ArcCot[x]] <= Pi/2 /; Element[x, Reals]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["ArcCot", "[", "x", "]"]], "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]], "/;", 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> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ≤ </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <abs /> <apply> <arccot /> <ci> x </ci> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29