(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 25512, 723] NotebookOptionsPosition[ 24173, 673] NotebookOutlinePosition[ 24569, 690] CellTagsIndexPosition[ 24526, 687] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["In\[EAcute]quations trigonom\[EAcute]triques", "Section", CellChangeTimes->{{3.414244465355582*^9, 3.414244471406033*^9}}], Cell[CellGroupData[{ Cell["\<\ R\[EAcute]soudre les in\[EAcute]quations trigonom\[EAcute]triques suivantes \ et repr\[EAcute]senter les solutions sur le cercle trigonom\[EAcute]trique\ \>", "Subsection", CellChangeTimes->{{3.414244475798534*^9, 3.414244499974628*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"<<", "trigo.m"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "=", "0"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "++"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"e", "[", "n", "]"}], "=", RowBox[{"HoldForm", "[", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], ">", RowBox[{"1", "/", "2"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "++"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"e", "[", "n", "]"}], "=", RowBox[{"HoldForm", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "2", "]"}], " ", RowBox[{"Cos", "[", RowBox[{"2", "x"}], "]"}]}], "<=", RowBox[{"-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "++"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"e", "[", "n", "]"}], "=", RowBox[{"HoldForm", "[", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "x"}], "]"}], ">", "0"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "++"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"e", "[", "n", "]"}], "=", RowBox[{"HoldForm", "[", RowBox[{ RowBox[{ RowBox[{"Tan", "[", RowBox[{"3", "x"}], "]"}], "+", "1"}], "\[GreaterEqual]", "0"}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "++"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"e", "[", "n", "]"}], "=", RowBox[{"HoldForm", "[", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "3", "]"}], RowBox[{"Tan", "[", RowBox[{"2", "x"}], "]"}]}], "<=", RowBox[{"-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Do", "[", RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"e", "[", "i", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}]}], "Input", CellOpen->False, CellChangeTimes->{{3.414244528971758*^9, 3.4142446697788153`*^9}, { 3.414244718833385*^9, 3.414244721799349*^9}, {3.414244922799654*^9, 3.414244993726994*^9}, {3.414245047995215*^9, 3.414245067064786*^9}, 3.414245101969924*^9, {3.4142451364924088`*^9, 3.414245136778253*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"1", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", TagBox[ RowBox[{ RowBox[{"sin", "(", "x", ")"}], ">", FractionBox["1", "2"]}], HoldForm]}], SequenceForm[1, ") ", HoldForm[Sin[$CellContext`x] > 1/2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.414245102747779*^9, 3.414245163859189*^9}}, FontSize->12], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"2", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", TagBox[ RowBox[{ RowBox[{ SqrtBox["2"], " ", RowBox[{"cos", "(", RowBox[{"2", " ", "x"}], ")"}]}], "\[LessEqual]", RowBox[{"-", "1"}]}], HoldForm]}], SequenceForm[2, ") ", HoldForm[Sqrt[2] Cos[2 $CellContext`x] <= -1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.414245102747779*^9, 3.414245163861807*^9}}, FontSize->12], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"3", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", TagBox[ RowBox[{ RowBox[{"cos", "(", RowBox[{"2", " ", "x"}], ")"}], ">", "0"}], HoldForm]}], SequenceForm[3, ") ", HoldForm[Cos[2 $CellContext`x] > 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.414245102747779*^9, 3.414245163864303*^9}}, FontSize->12], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"4", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", TagBox[ RowBox[{ RowBox[{ FormBox[ RowBox[{"tg", "(", RowBox[{"3", " ", "x"}], ")"}], TraditionalForm], "+", "1"}], "\[GreaterEqual]", "0"}], HoldForm]}], SequenceForm[4, ") ", HoldForm[Tan[3 $CellContext`x] + 1 >= 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.414245102747779*^9, 3.414245163866982*^9}}, FontSize->12], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"5", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", TagBox[ RowBox[{ RowBox[{ SqrtBox["3"], " ", FormBox[ RowBox[{"tg", "(", RowBox[{"2", " ", "x"}], ")"}], TraditionalForm]}], "\[LessEqual]", RowBox[{"-", "1"}]}], HoldForm]}], SequenceForm[5, ") ", HoldForm[Sqrt[3] Tan[2 $CellContext`x] <= -1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.414245102747779*^9, 3.414245163869698*^9}}, FontSize->12] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Solutions", "Subsubsection", CellChangeTimes->{{3.4142446776457443`*^9, 3.414244679346622*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"Ensemble", "[", RowBox[{ RowBox[{"ReleaseHold", "[", RowBox[{"e", "[", "i", "]"}], "]"}], ",", "x"}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"CercleTrigo", "[", RowBox[{"Cercle", "[", RowBox[{"Ensemble", "[", RowBox[{ RowBox[{"ReleaseHold", "[", RowBox[{"e", "[", "i", "]"}], "]"}], ",", "x"}], "]"}], "]"}], "]"}], "]"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}]], "Input", CellOpen->False, CellChangeTimes->{{3.414244713751153*^9, 3.4142447817906*^9}, { 3.414244828992095*^9, 3.414244843893322*^9}, {3.4142448789623127`*^9, 3.414244913769204*^9}, {3.414245031141571*^9, 3.414245035818625*^9}, { 3.414245178946658*^9, 3.414245196129344*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"1", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FormBox[ RowBox[{ RowBox[{ RowBox[{"2", " ", "\[Pi]", " ", "k"}], "+", FractionBox["\[Pi]", "6"]}], "<", "x", "<", RowBox[{ RowBox[{"2", " ", "\[Pi]", " ", "k"}], "+", FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "6"]}]}], TraditionalForm]}], SequenceForm[1, ") ", trigo`Ens[ And[ Element[ C[1], Integers], Inequality[ Rational[1, 6] Pi + 2 Pi C[1], Less, $CellContext`x, Less, Rational[5, 6] Pi + 2 Pi C[1]]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4142451964199533`*^9}], Cell[BoxData[ FormBox[ GraphicsBox[{CircleBox[{0, 0}], {InsetBox[ FractionBox["\[Pi]", "6"], {0.9660254037844386, 0.6}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "6"], {-0.9660254037844386, 0.6}], { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[13, 6] Pi, Rational[17, 6] Pi}, {6.8067840827778845`, 8.901179185171081}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}, { 0.8660254037844386, 0.5}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 3^Rational[1, 2], Rational[ 1, 2]}, {-0.8660254037844386, 0.5}]]}}}}, Axes->True], TraditionalForm]], "Print", CellChangeTimes->{3.4142451964386673`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"2", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FormBox[ RowBox[{ RowBox[{ RowBox[{"\[Pi]", " ", "k"}], "+", FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "8"]}], "\[LessEqual]", "x", "\[LessEqual]", RowBox[{ RowBox[{"\[Pi]", " ", "k"}], "+", FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "8"]}]}], TraditionalForm]}], SequenceForm[2, ") ", trigo`Ens[ And[ Element[ C[1], Integers], Inequality[ Rational[3, 8] Pi + Pi C[1], LessEqual, $CellContext`x, LessEqual, Rational[5, 8] Pi + Pi C[1]]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.414245196490678*^9}], Cell[BoxData[ FormBox[ GraphicsBox[{CircleBox[{0, 0}], {{InsetBox[ FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "8"], {0.4826834323650898, 1.0238795325112868`}], InsetBox[ FractionBox[ RowBox[{"11", " ", "\[Pi]"}], "8"], {-0.4826834323650898, -1.0238795325112868`}]}, {InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "8"], {-0.4826834323650898, 1.0238795325112868`}], InsetBox[ FractionBox[ RowBox[{"13", " ", "\[Pi]"}], "8"], {0.4826834323650898, -1.0238795325112868`}]}, {{ {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[11, 8] Pi, Rational[13, 8] Pi}, {4.319689898685965, 5.105088062083414}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{-Sin[Rational[1, 8] Pi], - Cos[Rational[1, 8] Pi]}, {-0.3826834323650898, -0.9238795325112867}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Sin[Rational[1, 8] Pi], -Cos[Rational[1, 8] Pi]}, { 0.3826834323650898, -0.9238795325112867}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[19, 8] Pi, Rational[21, 8] Pi}, {7.461282552275758, 8.246680715673207}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Sin[Rational[1, 8] Pi], Cos[Rational[1, 8] Pi]}, { 0.3826834323650898, 0.9238795325112867}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{-Sin[Rational[1, 8] Pi], Cos[ Rational[1, 8] Pi]}, {-0.3826834323650898, 0.9238795325112867}]]}}}}}, Axes->True], TraditionalForm]], "Print", CellChangeTimes->{3.4142451965210457`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"3", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FormBox[ RowBox[{ RowBox[{ RowBox[{"k", " ", "\[Pi]"}], "-", FractionBox["\[Pi]", "4"]}], "<", "x", "<", RowBox[{ RowBox[{"\[Pi]", " ", "k"}], "+", FractionBox["\[Pi]", "4"]}]}], TraditionalForm]}], SequenceForm[3, ") ", trigo`Ens[ And[ Element[ C[1], Integers], Inequality[ Rational[-1, 4] Pi + Pi C[1], Less, $CellContext`x, Less, Rational[1, 4] Pi + Pi C[1]]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4142451965707283`*^9}], Cell[BoxData[ FormBox[ GraphicsBox[{CircleBox[{0, 0}], {{InsetBox[ RowBox[{"-", FractionBox["\[Pi]", "4"]}], {0.8071067811865474, -0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "4"], {-0.8071067811865474, 0.8071067811865474}]}, {InsetBox[ FractionBox["\[Pi]", "4"], {0.8071067811865474, 0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "4"], {-0.8071067811865474, -0.8071067811865474}]}, {{ {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[3, 4] Pi, Rational[5, 4] Pi}, {2.356194490192345, 3.9269908169872414`}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{-2^Rational[-1, 2], 2^Rational[-1, 2]}, {-0.7071067811865475, 0.7071067811865475}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{-2^Rational[-1, 2], -2^ Rational[-1, 2]}, {-0.7071067811865475, -0.7071067811865475}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[7, 4] Pi, Rational[9, 4] Pi}, {5.497787143782138, 7.0685834705770345`}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{2^Rational[-1, 2], -2^Rational[-1, 2]}, { 0.7071067811865475, -0.7071067811865475}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{2^Rational[-1, 2], 2^Rational[-1, 2]}, {0.7071067811865475, 0.7071067811865475}]]}}}}}, Axes->True], TraditionalForm]], "Print", CellChangeTimes->{3.4142451966047*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"4", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FormBox[ RowBox[{ RowBox[{ FractionBox[ RowBox[{"k", " ", "\[Pi]"}], "3"], "-", FractionBox["\[Pi]", "12"]}], "\[LessEqual]", "x", "<", RowBox[{ FractionBox[ RowBox[{"\[Pi]", " ", "k"}], "3"], "+", FractionBox["\[Pi]", "6"]}]}], TraditionalForm]}], SequenceForm[4, ") ", trigo`Ens[ And[ Element[ C[1], Integers], Inequality[ Rational[-1, 12] Pi + Rational[1, 3] Pi C[1], LessEqual, $CellContext`x, Less, Rational[1, 6] Pi + Rational[1, 3] Pi C[1]]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.414245196642455*^9}], Cell[BoxData[ FormBox[ GraphicsBox[{CircleBox[{0, 0}], {{InsetBox[ RowBox[{"-", FractionBox["\[Pi]", "12"]}], {1.0659258262890683`, -0.3588190451025207}], InsetBox[ FractionBox["\[Pi]", "4"], {0.8071067811865474, 0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"7", " ", "\[Pi]"}], "12"], {-0.3588190451025207, 1.0659258262890683`}], InsetBox[ FractionBox[ RowBox[{"11", " ", "\[Pi]"}], "12"], {-1.0659258262890683`, 0.3588190451025207}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "4"], {-0.8071067811865474, -0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"19", " ", "\[Pi]"}], "12"], {0.3588190451025207, -1.0659258262890683`}]}, {InsetBox[ FractionBox["\[Pi]", "6"], {0.9660254037844386, 0.6}], InsetBox[ FractionBox["\[Pi]", "2"], {0, 1.1}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "6"], {-0.9660254037844386, 0.6}], InsetBox[ FractionBox[ RowBox[{"7", " ", "\[Pi]"}], "6"], {-0.9660254037844386, -0.6}], InsetBox[ FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "2"], {0, -1.1}], InsetBox[ FractionBox[ RowBox[{"11", " ", "\[Pi]"}], "6"], {0.9660254037844386, -0.6}]}, {{ {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[1, 4] Pi, Rational[1, 2] Pi}, {0.7853981633974483, 1.5707963267948966`}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{2^Rational[-1, 2], 2^Rational[-1, 2]}, {0.7071067811865475, 0.7071067811865475}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0, 1}]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[7, 12] Pi, Rational[5, 6] Pi}, {1.8325957145940461`, 2.6179938779914944`}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2]), Rational[1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2])}, {-0.2588190451025207, 0.9659258262890682}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 3^Rational[1, 2], Rational[ 1, 2]}, {-0.8660254037844386, 0.5}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[11, 12] Pi, Rational[7, 6] Pi}, { 2.8797932657906435`, 3.6651914291880923`}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2]), Rational[1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2])}, {-0.9659258262890682, 0.2588190451025207}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 3^Rational[1, 2], Rational[-1, 2]}, {-0.8660254037844386, -0.5}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[5, 4] Pi, Rational[3, 2] Pi}, {3.9269908169872414`, 4.71238898038469}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{-2^Rational[-1, 2], -2^ Rational[-1, 2]}, {-0.7071067811865475, -0.7071067811865475}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[{0, -1}]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[19, 12] Pi, Rational[11, 6] Pi}, {4.974188368183839, 5.759586531581287}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2]), Rational[-1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2])}, { 0.2588190451025207, -0.9659258262890682}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 3^Rational[1, 2], Rational[-1, 2]}, { 0.8660254037844386, -0.5}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[23, 12] Pi, Rational[13, 6] Pi}, {6.021385919380437, 6.8067840827778845`}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2]), Rational[-1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2])}, { 0.9659258262890682, -0.2588190451025207}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}, { 0.8660254037844386, 0.5}]]}}}}}, Axes->True], TraditionalForm]], "Print", CellChangeTimes->{3.414245196672717*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"5", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FormBox[ RowBox[{ RowBox[{ FractionBox[ RowBox[{"k", " ", "\[Pi]"}], "2"], "-", FractionBox["\[Pi]", "4"]}], "<", "x", "\[LessEqual]", RowBox[{ FractionBox[ RowBox[{"k", " ", "\[Pi]"}], "2"], "-", FractionBox["\[Pi]", "12"]}]}], TraditionalForm]}], SequenceForm[5, ") ", trigo`Ens[ And[ Element[ C[1], Integers], Inequality[ Rational[-1, 4] Pi + Rational[1, 2] Pi C[1], Less, $CellContext`x, LessEqual, Rational[-1, 12] Pi + Rational[1, 2] Pi C[1]]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.414245196722179*^9}], Cell[BoxData[ FormBox[ GraphicsBox[{CircleBox[{0, 0}], {{InsetBox[ RowBox[{"-", FractionBox["\[Pi]", "4"]}], {0.8071067811865474, -0.8071067811865474}], InsetBox[ FractionBox["\[Pi]", "4"], {0.8071067811865474, 0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "4"], {-0.8071067811865474, 0.8071067811865474}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "4"], {-0.8071067811865474, -0.8071067811865474}]}, {InsetBox[ RowBox[{"-", FractionBox["\[Pi]", "12"]}], {1.0659258262890683`, -0.3588190451025207}], InsetBox[ FractionBox[ RowBox[{"5", " ", "\[Pi]"}], "12"], {0.3588190451025207, 1.0659258262890683`}], InsetBox[ FractionBox[ RowBox[{"11", " ", "\[Pi]"}], "12"], {-1.0659258262890683`, 0.3588190451025207}], InsetBox[ FractionBox[ RowBox[{"17", " ", "\[Pi]"}], "12"], {-0.3588190451025207, -1.0659258262890683`}]}, {{ {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[1, 4] Pi, Rational[5, 12] Pi}, {0.7853981633974483, 1.3089969389957472`}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{2^Rational[-1, 2], 2^Rational[-1, 2]}, {0.7071067811865475, 0.7071067811865475}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2]), Rational[1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2])}, { 0.2588190451025207, 0.9659258262890682}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[3, 4] Pi, Rational[11, 12] Pi}, {2.356194490192345, 2.8797932657906435`}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{-2^Rational[-1, 2], 2^Rational[-1, 2]}, {-0.7071067811865475, 0.7071067811865475}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2]), Rational[1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2])}, {-0.9659258262890682, 0.2588190451025207}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[5, 4] Pi, Rational[17, 12] Pi}, { 3.9269908169872414`, 4.4505895925855405`}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{-2^Rational[-1, 2], -2^ Rational[-1, 2]}, {-0.7071067811865475, -0.7071067811865475}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[-1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2]), Rational[-1, 2] 2^Rational[-1, 2] (1 + 3^Rational[ 1, 2])}, {-0.2588190451025207, -0.9659258262890682}]]}}, { {RGBColor[0, 0, 1], Thickness[Large], CircleBox[{0, 0}, 1, NCache[{Rational[7, 4] Pi, Rational[23, 12] Pi}, {5.497787143782138, 6.021385919380437}]]}, {RGBColor[1, 0, 0], PointSize[Large], PointBox[ NCache[{2^Rational[-1, 2], -2^Rational[-1, 2]}, { 0.7071067811865475, -0.7071067811865475}]]}, {RGBColor[0, 0, 1], PointSize[Large], PointBox[ NCache[{Rational[1, 2] 2^Rational[-1, 2] (1 + 3^Rational[1, 2]), Rational[-1, 2] 2^Rational[-1, 2] (-1 + 3^Rational[1, 2])}, { 0.9659258262890682, -0.2588190451025207}]]}}}}}, Axes->True], TraditionalForm]], "Print", CellChangeTimes->{3.4142451967553883`*^9}] }, Open ]] }, Open ]] }, Closed]] }, Open ]] }, Open ]] }, WindowSize->{640, 750}, WindowMargins->{{269, Automatic}, {Automatic, 89}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (February 7, 2008)", StyleDefinitions->"stylemath.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 129, 1, 67, "Section"], Cell[CellGroupData[{ Cell[744, 28, 248, 4, 55, "Subsection"], Cell[CellGroupData[{ Cell[1017, 36, 2527, 77, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[3569, 117, 434, 13, 40, "Print"], Cell[4006, 132, 526, 16, 32, "Print"], Cell[4535, 150, 437, 13, 23, "Print"], Cell[4975, 165, 528, 16, 23, "Print"], Cell[5506, 183, 569, 18, 32, "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[6124, 207, 102, 1, 27, "Subsubsection"], Cell[CellGroupData[{ Cell[6251, 212, 960, 25, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[7236, 241, 748, 23, 39, "Print"], Cell[7987, 266, 849, 19, 365, "Print"], Cell[8839, 287, 790, 25, 39, "Print"], Cell[9632, 314, 1829, 42, 389, "Print"], Cell[11464, 358, 696, 22, 35, "Print"], Cell[12163, 382, 1734, 40, 365, "Print"], Cell[13900, 424, 796, 24, 39, "Print"], Cell[14699, 450, 4863, 105, 387, "Print"], Cell[19565, 557, 805, 25, 38, "Print"], Cell[20373, 584, 3736, 82, 377, "Print"] }, Open ]] }, Open ]] }, Closed]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)