(* 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[ 9228, 275] NotebookOptionsPosition[ 8501, 245] NotebookOutlinePosition[ 9148, 271] CellTagsIndexPosition[ 9080, 266] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Animation of Tan(", StyleBox["x", FontSlant->"Italic"], ")" }], "Title", TextAlignment->Center, FontSize->36, FontColor->RGBColor[1, 0, 0], CellTags->"sin(x)"], Cell["\<\ by Ruth Dover Illinois Mathematics and Science Academy\ \>", "Subsubtitle", CellChangeTimes->{{3.692573355804049*^9, 3.692573369405099*^9}}], Cell["\<\ Simply execute the one big cell below to see the graphics. Use the slider or \ click on the small \"+\" sign to the right to see more controls. The \ animation turns pink at a couple of spots to indicate that something's wrong. \ What happened?\ \>", "Text", CellChangeTimes->{{3.3954401057917356`*^9, 3.395440137793544*^9}, { 3.395440185466915*^9, 3.395440213139865*^9}, {3.395442988939897*^9, 3.3954430471919327`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"circlePts", "[", "\[Theta]_", "]"}], ":=", " ", "\n", "\t", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\n", "\t\t\t\t", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Thickness", "[", ".012", "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Thickness", "[", ".012", "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"Tan", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Thickness", "[", ".012", "]"}], ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"Tan", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Thickness", "[", ".012", "]"}], ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", " ", "\n", "\t\t\t\t\t", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"PointSize", "[", ".03", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"PointSize", "[", ".03", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"Tan", "[", "\[Theta]", "]"}]}], "}"}], "]"}]}], "}"}]}], " ", "}"}], ",", RowBox[{"AspectRatio", " ", "\[Rule]", " ", RowBox[{"4", "/", "3"}]}], ",", " ", RowBox[{"Axes", " ", "\[Rule]", " ", "Automatic"}], ",", RowBox[{"Ticks", " ", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}], " ", ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", " ", "1.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1.9"}], ",", " ", "1.9"}], "}"}]}], "}"}]}], ",", "\n", "\t\t\t", RowBox[{"Epilog", "\[Rule]", RowBox[{"Text", "[", RowBox[{ RowBox[{"StringForm", "[", RowBox[{"\"\<\[Theta] = ``\>\"", ",", " ", RowBox[{"TraditionalForm", "[", "\[Theta]", "]"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1.2"}], ",", " ", "1.5"}], "}"}]}], "]"}]}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"tanPlot", "[", "\[Theta]_", "]"}], ":=", RowBox[{"Plot", "[", RowBox[{ RowBox[{"Tan", "[", "x", "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", RowBox[{"2", "\[Pi]"}]}], "}"}], ",", "\n", "\t ", RowBox[{"Ticks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", FractionBox["\[Pi]", "2"], ",", "\[Pi]", ",", FractionBox[ RowBox[{"3", " ", "\[Pi]"}], "2"], ",", RowBox[{"2", " ", "\[Pi]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", " ", "1"}], "}"}]}], "}"}]}], ",", RowBox[{"PlotRange", " ", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", " ", "2"}], "}"}]}], ",", "\n", "\t\t", RowBox[{"AxesLabel", " ", "\[Rule]", RowBox[{"{", RowBox[{"\"\<\[Theta]\>\"", ",", " ", "None"}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", RowBox[{"\[Pi]", "/", "2"}]}], ",", "\n", "\t\t", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"PointSize", "[", ".03", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"\[Theta]", ",", " ", RowBox[{"Tan", "[", "\[Theta]", "]"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Thickness", "[", ".012", "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"\[Theta]", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Theta]", ",", " ", RowBox[{"Tan", "[", "\[Theta]", "]"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", " ", RowBox[{"Text", "[", RowBox[{"\"\<\!\(\* StyleBox[\"y\", FontSlant->\"Italic\"]\)=tan(\[Theta])\>\"", ",", " ", RowBox[{"{", RowBox[{"5.8", ",", " ", "1.8"}], "}"}]}], "]"}]}], "}"}]}]}], "]"}]}], ";"}], "\n", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"GraphicsGrid", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"circlePts", "[", "\[Theta]", "]"}], ",", RowBox[{"tanPlot", "[", "\[Theta]", "]"}]}], "}"}], "}"}], ",", RowBox[{"Spacings", "\[Rule]", "50"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"\[Theta]", ",", " ", "0", ",", " ", RowBox[{"2", "\[Pi]"}], ",", " ", FractionBox["\[Pi]", "12"]}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.395442431576062*^9, 3.395442461778276*^9}, { 3.395442494392292*^9, 3.395442670205752*^9}, {3.3954427017551823`*^9, 3.3954427815162277`*^9}, 3.3954428693717937`*^9, {3.395442940456918*^9, 3.39544295362847*^9}, {3.69257338352663*^9, 3.692573388363247*^9}}] }, Open ]] }, WindowSize->{825, 721}, WindowMargins->{{4, Automatic}, {Automatic, 1}}, DockedCells->(FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, Placeholder]}]& ), PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, FrontEndVersion->"11.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \ 21, 2016)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "sin(x)"->{ Cell[567, 22, 185, 9, 83, "Title", CellTags->"sin(x)"]} } *) (*CellTagsIndex CellTagsIndex->{ {"sin(x)", 8995, 260} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 185, 9, 83, "Title", CellTags->"sin(x)"], Cell[755, 33, 151, 4, 49, "Subsubtitle"], Cell[909, 39, 439, 8, 68, "Text"], Cell[1351, 49, 7134, 193, 420, "Input"] }, Open ]] } ] *)