(* 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[      7201,        245]
NotebookOptionsPosition[      6565,        221]
NotebookOutlinePosition[      7000,        238]
CellTagsIndexPosition[      6957,        235]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Transformations of Sine", "Title",
 CellChangeTimes->{{3.409530769294641*^9, 3.409530771013706*^9}, {
  3.692573877833417*^9, 3.692573883186928*^9}},
 TextAlignment->Center,
 FontSize->36],

Cell["\<\
by Ruth Dover
Illinois Mathematics and Science Academy\
\>", "Text",
 CellChangeTimes->{{3.6925737821484613`*^9, 3.692573799473075*^9}}],

Cell["\<\
\tThis notebook will allow you to look at all of the basic transformations at \
one time.  We'll first consider the following sine function:\
\>", "Text",
 CellChangeTimes->{{3.409530855597342*^9, 3.409530892565982*^9}},
 TextAlignment->Left,
 FontSize->16],

Cell[TextData[{
 StyleBox["y",
  FontSlant->"Italic"],
 " = ",
 StyleBox["A",
  FontSlant->"Italic"],
 " sin[ ",
 StyleBox["B",
  FontSlant->"Italic"],
 " (",
 StyleBox["x",
  FontSlant->"Italic"],
 " + ",
 StyleBox["C",
  FontSlant->"Italic"],
 ") ] + ",
 StyleBox["D.",
  FontSlant->"Italic"],
 " "
}], "Text",
 TextAlignment->Center,
 FontSize->16],

Cell[TextData[{
 "It should be noted that the parameters affect the graph of ",
 " ",
 StyleBox["y",
  FontSlant->"Italic"],
 " = ",
 StyleBox["A",
  FontSlant->"Italic"],
 " cos[ ",
 StyleBox["B",
  FontSlant->"Italic"],
 " (",
 StyleBox["x",
  FontSlant->"Italic"],
 " + ",
 StyleBox["C",
  FontSlant->"Italic"],
 ") ] + ",
 StyleBox["D ",
  FontSlant->"Italic"],
 "in the same manner."
}], "Text"],

Cell[TextData[{
 StyleBox["Note:", "Input"],
 "  In this notebook, in each case, the primary function ",
 StyleBox["y",
  FontSlant->"Italic"],
 " = sin(",
 StyleBox["x)",
  FontSlant->"Italic"],
 ", is graphed in a yellowish color along with the graph in question which is \
shown in blue.  This is to allow you to compare them more easily.  You may \
edit the ",
 StyleBox["xmin",
  FontSlant->"Italic"],
 " and ",
 StyleBox["xmax",
  FontSlant->"Italic"],
 " if necessary."
}], "Text",
 CellChangeTimes->{
  3.6925739284026747`*^9, {3.6925740231531057`*^9, 3.692574030454411*^9}}],

Cell["\<\
To \"execute\" a command, press \[ShiftKey]-\[EnterKey]. Then use the sliders \
as you wish.\
\>", "Text",
 CellChangeTimes->{
  3.692573991201624*^9, {3.6925740617976723`*^9, 3.6925740671865053`*^9}, {
   3.692574104661603*^9, 3.692574111085313*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"xmin", "=", 
   RowBox[{
    RowBox[{"-", "2"}], " ", "\[Pi]"}]}], ";", 
  RowBox[{"xmax", "=", 
   RowBox[{"2", " ", "\[Pi]"}]}], ";"}], "\n", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Sin", "[", "x", "]"}], ",", 
       RowBox[{
        RowBox[{"A", " ", 
         RowBox[{"Sin", "[", 
          RowBox[{"B", 
           RowBox[{"(", 
            RowBox[{"x", "+", "C"}], ")"}]}], "]"}]}], "+", "D"}]}], "}"}], 
     ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "xmin", ",", "xmax"}], "}"}], ",", 
     RowBox[{"Ticks", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Range", "[", 
         RowBox[{"xmin", ",", "xmax", ",", 
          FractionBox["\[Pi]", "2"]}], "]"}], ",", "Automatic"}], "}"}]}], 
     ",", 
     RowBox[{"ImageSize", "\[Rule]", "600"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"Orange", ",", "Thick"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"Blue", ",", "Thick"}], "}"}]}], "}"}]}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "6"}], ",", " ", "6"}], "}"}]}], ",", 
     RowBox[{"PlotLabel", "\[Rule]", 
      RowBox[{"Style", "[", 
       RowBox[{
        RowBox[{"StringForm", "[", 
         RowBox[{"\"\<\!\(\*
StyleBox[\"y\",
FontSlant->\"Italic\"]\)\!\(\*
StyleBox[\" \",
FontSlant->\"Italic\"]\)= ``\>\"", ",", 
          RowBox[{
           RowBox[{"A", " ", 
            RowBox[{"Sin", "[", 
             RowBox[{"B", 
              RowBox[{"(", 
               RowBox[{"x", "+", "C"}], ")"}]}], "]"}]}], "+", "D"}]}], " ", 
         "]"}], ",", 
        RowBox[{"FontSize", "\[Rule]", "24"}], ",", 
        RowBox[{"FontColor", "\[Rule]", "Blue"}]}], "]"}]}]}], "]"}], ",", 
   " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"A", ",", " ", "1"}], "}"}], ",", 
     RowBox[{"-", "3"}], ",", " ", "3", ",", " ", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", " ", 
   
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"B", ",", " ", "1"}], "}"}], ",", " ", 
     RowBox[{"-", "4"}], ",", " ", "4", ",", " ", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", " ", 
   
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"C", ",", " ", "0"}], "}"}], ",", " ", 
     RowBox[{"-", "\[Pi]"}], ",", " ", "\[Pi]", ",", " ", 
     RowBox[{"\[Pi]", "/", "12"}], ",", " ", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", " ", 
   
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"D", ",", " ", "0"}], "}"}], ",", " ", 
     RowBox[{"-", "3"}], ",", " ", "3", ",", " ", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.394548152199766*^9, 3.39454819728354*^9}, {
  3.3945482381791143`*^9, 3.394548241561059*^9}, {3.394548272985188*^9, 
  3.3945482819301577`*^9}, {3.39454832564675*^9, 3.39454841719862*^9}, {
  3.409530944368369*^9, 3.40953099233038*^9}, {3.409531045678389*^9, 
  3.409531166681773*^9}, {3.4095324420913982`*^9, 3.409532471593855*^9}, {
  3.4095325089852552`*^9, 3.409532522624275*^9}, {3.409532572196878*^9, 
  3.4095325794139147`*^9}, {3.409532661535019*^9, 3.409532669077334*^9}, {
  3.409532724025926*^9, 3.4095327601294613`*^9}, {3.409532867951651*^9, 
  3.409532883879024*^9}, {3.4095334828898478`*^9, 3.409533543735279*^9}, {
  3.409533585603795*^9, 3.409533596383028*^9}, {3.409533800699819*^9, 
  3.409533824781933*^9}, {3.40953385610081*^9, 3.409533857741828*^9}, {
  3.443658388350618*^9, 3.443658391500454*^9}}]
}, Open  ]]
},
WindowSize->{786, 709},
WindowMargins->{{4, Automatic}, {Automatic, 3}},
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->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 194, 4, 83, "Title"],
Cell[764, 28, 146, 4, 49, "Text"],
Cell[913, 34, 267, 6, 55, "Text"],
Cell[1183, 42, 351, 21, 33, "Text"],
Cell[1537, 65, 400, 21, 30, "Text"],
Cell[1940, 88, 583, 19, 69, "Text"],
Cell[2526, 109, 261, 6, 30, "Text"],
Cell[2790, 117, 3759, 101, 235, "Input"]
}, Open  ]]
}
]
*)