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Find a polar equation of the form r = f(theta) for the curve represented by the given Cartesian...

Question:

Find a polar equation of the form {eq}r = f( \theta) {/eq} for the curve represented by the given Cartesian equation {eq}\displaystyle x = 3 {/eq}.

Cartesian to Polar Equation:

Converting Cartesian equations into polar equations has lots of different applications in calculus.

To transform a Cartesian equation into a polar equation, we make use of the following identitites:

{eq}x = r \cos \theta {/eq}

{eq}y = r \sin \theta {/eq}

{eq}x^2 + y^2 = r^2 {/eq}

Answer and Explanation: 1

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To transform the given Cartesian equation into a polar equation, we plug in {eq}x = r \cos \theta {/eq}:

{eq}\begin{align*} \displaystyle x & = 3...

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Graphing Functions in Polar Coordinates: Process & Examples

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


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