Joslyn Landry

2023-03-24

How to graph $r=5\mathrm{sin}\theta$?

bootjietz0r

Beginner2023-03-25Added 7 answers

How polar coordinates relate to one another $(r,\theta )$ and rectangular Cartesian coordinates $(x,y)$ are given by

$x=r\mathrm{cos}\theta$ and $y=r\mathrm{sin}\theta$ or $r}^{2}={x}^{2}+{y}^{2$

Hence $r=5\mathrm{sin}\theta$ can be written as

${r}^{2}=5r\mathrm{sin}\theta$

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

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

$x=r\mathrm{cos}\theta$ and $y=r\mathrm{sin}\theta$ or $r}^{2}={x}^{2}+{y}^{2$

Hence $r=5\mathrm{sin}\theta$ can be written as

${r}^{2}=5r\mathrm{sin}\theta$

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

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

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