Sine: Inequalities (formula 01.06.29.0004)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Inequalities

http://functions.wolfram.com/01.06.29.0004.01

Input Form

Sin[x] >= x (1 - x/Pi) /; 0 <= x <= Pi

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sin", "[", "x", "]"]], "\[GreaterEqual]", RowBox[List["x", " ", RowBox[List["(", RowBox[List["1", "-", FractionBox["x", "\[Pi]"]]], ")"]]]]]], "/;", RowBox[List["0", "\[LessEqual]", "x", "\[LessEqual]", "\[Pi]"]]]]]]

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> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ≥ </mo> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> x </mi> <mi> π </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> ≤ </mo> <mi> x </mi> <mo> ≤ </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <sin /> <ci> x </ci> </apply> <apply> <times /> <ci> x </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> x </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 0 </cn> <ci> x </ci> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29