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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Other information > Value properties





http://functions.wolfram.com/01.07.33.0001.01









  


  








Input Form





Implies[Element[x, Rationals] && Element[Cos[x Degree], Rationals], Cos[x] == 0 || Cos[x] == 1/2 || Cos[x] == -(1/2) || Cos[x] == 1 || Cos[x] == -1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["x", "\[Element]", "Rationals"]], "\[And]", RowBox[List[RowBox[List["Cos", "[", RowBox[List["x", " ", "Degree"]], "]"]], "\[Element]", "Rationals"]]]], ")"]], "\[Implies]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", "0"]], "\[Or]", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", FractionBox["1", "2"]]], "\[Or]", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", RowBox[List["-", FractionBox["1", "2"]]]]], "\[Or]", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", "1"]], "\[Or]", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "1"]]]]]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mo> &#176; </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#62755; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <implies /> <apply> <and /> <apply> <in /> <ci> x </ci> <rationals /> </apply> <apply> <in /> <apply> <cos /> <apply> <times /> <ci> x </ci> <ci> Degree </ci> </apply> </apply> <rationals /> </apply> </apply> <apply> <or /> <apply> <eq /> <apply> <cos /> <ci> x </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <cos /> <ci> x </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <eq /> <apply> <cos /> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <eq /> <apply> <cos /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <cos /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List["Implies", "[", RowBox[List[RowBox[List[RowBox[List["x", "\[Element]", "Rationals"]], "&&", RowBox[List[RowBox[List["Cos", "[", RowBox[List["x", " ", "\[Degree]"]], "]"]], "\[Element]", "Rationals"]]]], ",", RowBox[List[RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", "0"]], "||", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", FractionBox["1", "2"]]], "||", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", RowBox[List["-", FractionBox["1", "2"]]]]], "||", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", "1"]], "||", RowBox[List[RowBox[List["Cos", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "1"]]]]]]]], "]"]]]]


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





2002-12-18