# Listplot of a function Sin[2 x] vs Cos[2 x] when x is real and when x is random variable?

Listplot of a function Sin[2 x] vs Cos[2 x] when x is real and when x is a random variable? what is the effect of phase in the plot?

• Show us your Mathematica code, please. Apr 19, 2020 at 13:02

Clear["Global*"]

SeedRandom[1234];
data = {Cos[2 #], Sin[2 #]} & /@
RandomReal[{0, Pi}, 64];

{{ParametricPlot[
{Cos[2 x], Sin[2 x]}, {x, 0, Pi},
PlotRange -> {{-1.05, 1.05}, {-1.05, 1.05}}],
ListPlot[
Table[{Cos[2 x], Sin[2 x]}, {x, 0, Pi, Pi/64}],
PlotRange -> {{-1.05, 1.05}, {-1.05, 1.05}},
AspectRatio -> 1]},
{ListPlot[data,
PlotRange -> {{-1.05, 1.05}, {-1.05, 1.05}},
AspectRatio -> 1],
ListCurvePathPlot[data,
PlotRange -> {{-1.05, 1.05}, {-1.05, 1.05}}]}} //
Grid


### ListLinePlot

table1 = Table[{Sin[2 x], Cos[2 x]}, {x, Range[0, 2 Pi, 2 Pi/16]}];

SeedRandom[1]
table2 = Table[{Sin[2 x], Cos[2 x]}, {x, RandomReal[{0, 2 Pi}, 16]}];

ListLinePlot[{table1, table2},
PlotStyle -> {Red, Blue},
PlotMarkers -> {Automatic, 15},
AspectRatio -> 1,
Frame -> True,
Axes -> False,
Epilog -> Circle[],
PlotLegends -> {"table1", "table2"}]


### ParametricPlot

ClearAll[rR]
rR := RandomReal[{-.5, .5}];

SeedRandom[1]
Show[ParametricPlot[{Sin[2 x], Cos[2 x]}, {x, 0, 2 Pi},
PlotStyle -> Red, PlotRangePadding -> Scaled[.2]],
ParametricPlot[{Sin[2 (x + (rr = rR))], Cos[2 (x + rr)]}, {x, 0,
2 Pi}, PlotStyle -> Opacity[.7, Blue], MaxRecursion -> 0,
PlotPoints -> 20], ImageSize -> 400]


SeedRandom[1]
Show[ParametricPlot[{Sin[2 x], Cos[2 x]}, {x, 0, 2 Pi},
PlotStyle -> Red, PlotRangePadding -> Scaled[.2]],
ParametricPlot[{Sin[2 (x + (rr = rR))], Cos[2 (x + rr)]}, {x, 0,
2 Pi}, PlotStyle -> Opacity[.3, Blue], MaxRecursion -> 0,
PlotPoints -> 1000], ImageSize -> 400]
`