File:Circular Harmonic Y(3,0) Polar Diff.svg

${\displaystyle r=r_{0}+r_{1}L_{3}^{0}\left(\cos \theta \right),}$

${\displaystyle r_{0}=1,\quad r_{1}=0.25}$

${\displaystyle \left(0,r1+r0\right)\,,}$

${\displaystyle \cos \left(\theta \right)=-{\frac {1}{\sqrt {5}}}\,}$

${\displaystyle \left(r0-r1,\pi \right)\,,}$

${\displaystyle \cos \left(\theta \right)={\frac {1}{\sqrt {5}}}\,}$

${\displaystyle \theta ={\frac {\pi }{2}},{\frac {3\pi }{2}},}$

${\displaystyle \cos \left(\theta \right)=\pm {\sqrt {\frac {3}{5}}}\,}$