Cosine: Inequalities (formula 01.07.29.0004)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Inequalities

http://functions.wolfram.com/01.07.29.0004.01

Input Form

Abs[Cos[z]] <= Cosh[Abs[z]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], "\[LessEqual]", RowBox[List["Cosh", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ≤ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <leq /> <apply> <abs /> <apply> <cos /> <ci> z </ci> </apply> </apply> <apply> <cosh /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], "\[LessEqual]", RowBox[List["Cosh", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]]]]

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

2001-10-29