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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View this answerGiven 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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Chapter 24 / Lesson 1Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.