How do you graph $r = 2 + sin θ$ $r=2+sintheta$ ?

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Answer 1 · 2016-10-10T21:54:59

${(x^{2} + y^{2} - y)}^{2} - 4 (x^{2} + y^{2}) = 0$ $(x^2+y^2-y)^2-4(x^2+y^2)=0$

Using the pass equations

${(x=rcostheta),(y=rsintheta):}$

we have

$r=2+y/r$ or

$r^2=2r+y$ or

$x^2+y^2-y=2sqrt(x^2+y^2)$ squaring both sides

$(x^2+y^2-y)^2-4(x^2+y^2)=0$

Attached a plot

enter image source here

How do you graph r=2+sinthetar=2+sinθr=2+sintheta?