How do you graph $r = 5 sin θ$ $r= 5 sin theta$ ?

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Answer 1 · 2016-10-20T09:41:24

$x^{2} + y^{2} - 5 y = 0$ $x^2+y^2-5y=0$

The relation between polar coordinates $(r, θ)$ $(r,theta)$ and rectangular Cartesian coordinates $(x, y)$ $(x,y)$ are given by

$x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$ or $r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$

Hence $r = 5 sin θ$ $r=5sintheta$ can be written as

$r^{2} = 5 r sin θ$ $r^2=5rsintheta$

or $x^{2} + y^{2} = 5 y$ $x^2+y^2=5y$

or $x^{2} + y^{2} - 5 y = 0$ $x^2+y^2-5y=0$

How do you graph r=5sinθr= 5 sin theta?