How can I plot such a parametrized curve:
$r = 2\cos t + \sin t$
$\theta = t$
$\phi = \sin 10t$
where $0<t<\pi/2$.
In the documentation only has been discussed parametric plot in Cartesian coordinates.
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5 
3 Answers
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If you have version 9+ you can use:
ParametricPlot3D[ Evaluate[CoordinateTransform["Spherical" -> "Cartesian",{2 Cos[t]+Sin[t],t,Sin[10 t]}]], {t,0,Pi/2}] 
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- covert your spherical parametrized curve into cartesian parametrized curve with formulas:
$$\begin{cases} x&=r\sin\theta\cos\varphi\\ y&=r\sin\theta\sin\varphi\\ z&=r\cos\theta \end{cases}$$
in Mathematica better use some function for this:
ConvertToCartesianParametr[r_, theta_,phi_] := {r*Sin[theta]*Cos[phi], *Sin[theta]*Sin[phi], r*Cos[theta]} use
ParametricPlot3Das mentioned by Alexei Boulbitchr = 2*Cos[t] + Sin[t]; theta = t; phi = Sin[10*t]; ParametricPlot3D[ConvertToCartesianParametr[r, theta, phi], {t, 0, 2*Pi}]
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1 It is just the answer of @kguler, with a slight modification. Try this:
ParametricPlot3D[{(2 + Cos[t] + Sin[t])*Sin[t]* Cos[Sin[10 t]], (2 + Cos[t] + Sin[t])*Sin[t]* Sin[Sin[10 t]], (2 + Cos[t] + Sin[t])*Cos[t]}, {t, 0, 2 Pi}] 
A nice curve it is. Have fun!
- 4$\begingroup$ If you have version 9+ you can use:
ParametricPlot3D[Evaluate[CoordinateTransform[ "Spherical" -> "Cartesian",{2 Cos[t]+Sin[t],t,Sin[10 t]}]],{t,0,Pi/2}]$\endgroup$chuy– chuy2014-10-01 14:19:19 +00:00Commented Oct 1, 2014 at 14:19
RevolutionPlot3D[{2 + Cos[t] + Sin[t], t, Sin[10 t]}, {t, 0, 2 Pi}]give what you need? $\endgroup$ParametricPlot3D[{2 + Cos[t] + Sin[t], t, Sin[10 t]}, {t, 0, 2 Pi}]? $\endgroup$