# Find a Cartesian equation for the curve described by the given polar equation. {eq}r=5\sin(\theta) {/eq}

## Question:

Find a Cartesian equation for the curve described by the given polar equation.

{eq}r=5\sin(\theta) {/eq}

## Polar to Cartesian:

Assume a polar equation given in the form,

{eq}r=f(\theta){/eq}

We need to bring the equation in the form of {eq}g(r \cos \theta, r \sin \theta)=0{/eq}

Then substitute {eq}r \cos \theta=x{/eq} and {eq}r \sin \theta=y{/eq}

Also note that {eq}r^2=x^2+y^2{/eq}

Hence we get the Cartesian equation {eq}g(x,y)=0{/eq}

## Answer and Explanation: 1

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Given polar equation,

{eq}\begin{align} r &=5 \sin \theta \\ r^2 &=5 r\sin \theta &&....\text{Multiplying by r}\\ x^2+y^2 &= 5y...

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