Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Sinusoid

Packages and Initializations

Needs["ParaPlot`"]
Needs["PlaneCurveFormulas`"]
Needs["PlaneCurveGenerator`"]

Sinusoid illustration

Plot[Sin[x], {x, 0, 2*Pi}, AspectRatio -> Automatic, 
        Ticks -> {Range[-2*Pi, 2*Pi, Pi], {-1,  .5, 0,  .5, 
              1}}];

Sinusoid generation animation

SineGenerator[{0,2.5},LastFrameOnly->True];

Helix projection illustration

Needs["RuledSurfacePlot`"]

Needs["Graphics`Graphics3D`"]	(* 0200-518 *)

?Helicoid

Sinusoid is the orthogonal projection of a helix.

Shadow[
      Helicoid[3, 1.5, 2.5, PlotPoints -> {61, 4}, 
        HiddenSurface -> False, DisplayFunction -> Identity], 
      ZShadow -> False, 
      ViewPoint -> {1.757, -2.189, 1.889}];

graphics gallery

Parallels of six trig functions and their inverse.

Clear[curves]
curves = (Parallel[#1, t, {-1, 1}] &) /@ {{t, Sin[t]}, {t, 
            Cos[t]}, {t, Tan[t]}, {t, Csc[t]}, {t, Sec[t]}, {t, Cot[t]}, {t, 
            ArcSin[t]}, {t, ArcCos[t]}, {t, ArcTan[t]}, {t, ArcCsc[t]}, {t, 
            ArcSec[t]}, {t, ArcCot[t]}}; 
curves = Partition[Flatten[curves], 2];

Off[ParametricPlot::"pptr"]
ParametricPlot[
        Evaluate[
          curves], {t, -2 π, -((3 π)/2), -π, -(π/2), 0, (π/2), π, ((3 π)/2), 2 π}, 
        PlotRange -> {{-2 π, 2 π}, {-4, 4}}, 
        AspectRatio -> Automatic, 
        Ticks -> {Table[i π, {i, 5}], Range[3]}, 
        PlotStyle -> {Hue[0], Hue[ .65], Hue[ .35, 1,  .5], 
            Hue[0.1, 1, 1], Hue[ .75,  .8, 1], 
            Hue[ .35, 1,  .8]}];
On[ParametricPlot::"pptr"]