x ((Pi - x)/Pi) < Sin[x] < x (((Pi - x) (2 Pi - x))/Pi^2) /; Element[x, Reals] && 0 < x < Pi

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["x", " ", FractionBox[RowBox[List["\[Pi]", "-", "x"]], "\[Pi]"]]], "<", RowBox[List["Sin", "[", "x", "]"]], "<", RowBox[List["x", " ", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", "-", "x"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["2", "\[Pi]"]], "-", "x"]], ")"]]]], SuperscriptBox["\[Pi]", "2"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", "x", "<", "\[Pi]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> &#960; </mi> </mfrac> <mo> &lt; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mi> x </mi> <mo> &lt; </mo> <mi> &#960; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <ci> x </ci> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <ci> x </ci> </apply> <apply> <times /> <ci> x </ci> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <ci> x </ci> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["x", " ", RowBox[List["(", RowBox[List["\[Pi]", "-", "x"]], ")"]]]], "\[Pi]"], "<", RowBox[List["Sin", "[", "x", "]"]], "<", FractionBox[RowBox[List["x", " ", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", "-", "x"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Pi]"]], "-", "x"]], ")"]]]], ")"]]]], SuperscriptBox["\[Pi]", "2"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", "x", "<", "\[Pi]"]]]]]]]]

2002-12-18