How do you graph $r = 3 sin θ$ $r=3sintheta$ ?

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Answer 1 · 2017-01-04T08:08:42

$x^{2} + y^{2} = 3 y$ $x^2+y^2=3y$

The relation between polar coordinates $(r, θ)$ $(r,theta)$ and Cartesian coordinates $(x, y)$ $(x,y)$ is

$x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$ i.e. $r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$ and $\frac{y}{x} = tan θ$ $y/x=tantheta$

Hence $r = 3 sin θ$ $r=3sintheta$ can be written as $r^{2} = 3 r sin θ$ $r^2=3rsintheta$ i.e.

$x^{2} + y^{2} = 3 y$ $x^2+y^2=3y$ , which is the equation of a circle.
graph{x^2+y^2=3y [-5.375, 4.625, -0.54, 4.46]}

How do you graph r=3sinθr=3sintheta?