Consider the equation in polar coordinates: r^2 = 4 What is the equation in Cartesian...


Consider the equation in polar coordinates:

{eq}r^2 = 4 {/eq}

What is the equation in Cartesian (rectangular) coordinates equivalent to this equation in polar coordinates?

Polar Curves

A polar curve given as {eq}\displaystyle r=f(\theta), a\leq \theta \leq b, {/eq} is converted to the Cartesian form {eq}\displaystyle g(x,y)=0 {/eq}

by using the polar-Cartesian conversion equations

{eq}\displaystyle x=r\cos \theta, y=r\sin\theta \text{ and }x^2+y^2=r^2. {/eq}

Sometimes it is easier to recognize a curve given in polar coordinates if it si converted to Cartesian coordinates.

Answer and Explanation: 1

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The Cartesian form of the polar equation {eq}\displaystyle r^2=4, {/eq} for any polar angle {eq}\displaystyle \theta, {/eq}

is obtain by writing...

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Learn more about this topic:

Graphing Functions in Polar Coordinates: Process & Examples


Chapter 24 / Lesson 1

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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