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Bug introduced in 8.0.4 or earlier and persists through 12.0.0. Fixed in 12.1.0. Affects only Windows.

I just tried to plot Tan[t]^4 as a polar plot and got... nothing.

PolarPlot[Tan[t]^2, {t, 0, 2 Pi}]

Works:

enter image description here

PolarPlot[Tan[t]^4, {t, 0, 2 Pi}]

Doesn't work:

enter image description here

Changing the 4 to a 4. to enforce numerical results doesn't change anything.

Am I doing something wrong? Is this a bug? In case it matters:

$Version
"11.0.0 for Microsoft Windows (64-bit) (July 28, 2016)"
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  • 1
    $\begingroup$ PolarPlot[Tan[t]^4, {t, 0, 2 Pi}] works in 11.1 for macOS for me. Are you able to upgrade? $\endgroup$ – ktm Apr 6 '17 at 14:05
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    $\begingroup$ @J.M. I tried that. In that instance it seems to attempt to plot the line (I see a narrow blue line about the axis), but the PlotRange is 1.5x10^13, so it is less than useful. Playing around with PlotRange didn't get me very far. $\endgroup$ – ktm Apr 6 '17 at 14:18
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    $\begingroup$ @user, well, Cases[Normal[PolarPlot[Tan[t]^4, {t, 0, 2 π}]], Line[l_] :> l, ∞][[1]] shows that a line is getting plotted, but a look at the values of the coordinates tells me that the automatic PlotRange determined is way off the actual extent of the curve. $\endgroup$ – J. M.'s technical difficulties Apr 6 '17 at 14:22
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    $\begingroup$ PolarPlot[Tan[t]^3, {t, 0, 2 Pi}, PlotPoints -> 50] /. x_Real :> Clip[x, {-500, 500}] an extremely stupid solution, but possibly works sometimes, at least here...... some extra optimization of Clip's value may make the process more automated. $\endgroup$ – Wjx Apr 6 '17 at 14:23
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    $\begingroup$ PolarPlot[Tan[t]^4, {t, 0, 2 Pi}, PlotPoints -> 100, MaxRecursion -> 1] $\endgroup$ – chuy Apr 6 '17 at 15:08
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This was originally confirmed by Wolfram Support to be a bug and has now been fixed in 12.1.0:

PolarPlot[Tan[t]^4, {t, 0, 2 Pi}]

enter image description here

This also fixes the following snippets from the comments:

ParametricPlot[Tan[t]^4 AngleVector[t], {t, 0, 2 Pi}]

enter image description here

PolarPlot[Tan[t]^(2 + 5 10^(-15)), {t, 0, 2 Pi}]

enter image description here

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