How do I convert the polar equation $r=10 sin theta$ to its Cartesian equivalent?

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How do I convert the polar equation $r=10 sin theta$ to its Cartesian equivalent?

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Answer 1 · 2014-10-02T21:09:10

Cartesian coordinates, also known as Rectangular coordinates, are defined in terms of $x$ and $y$ . So, for this problem $theta$ has to be eliminated/converted using basic foundations described by the unit circle and right triangle trigonometry.

$r=10sin(theta)$

Remember that ...

$x=r*cos(theta)$

$y=r*sin(theta)$

$r^2=x^2+y^2$

Multiply both sides of the equation by $r$

$r*r=10r*sin(theta)$

$r^2=10r*sin(theta)$

$x^2+y^2=10r*sin(theta)$

Use the fact that $y=r*sin(theta)$ to make a substitution.

$x^2+y^2=10y$

$x^2+y^2-10y=0$

The above equation is the Cartesian/Rectangular coordinate equivalent to the given Polar equation.

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How do I convert the polar equation $r=10 sin theta$ to its Cartesian equivalent?

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