Copyright

Find a cartesian equation for the curve represented by the following polar equation. r = 1 / ( 4...

Question:

Find a cartesian equation for the curve represented by the following polar equation. {eq}r = \frac{1}{(4-sin(\theta))} {/eq}

Polar to Cartesian Equation:

A polar equation is converted to a Cartesian equation by utilizing the following formulas:

{eq}\cos(\theta) = \displaystyle \frac{x}{r} {/eq}

{eq}\sin(\theta) = \displaystyle \frac{y}{r} {/eq}

Since the equation will contain {eq}r {/eq}, which is still part of polar coordinates, the equation is converted into a Cartesian equation by using:

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

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

First, we will substitute {eq}\sin(\theta) = \displaystyle \frac{y}{r} {/eq} and rewrite the equation accordingly:

{eq}\begin{align*} \displaystyle...

See full answer below.


Learn more about this topic:

Loading...
Polar Coordinates: Definition, Equation & Examples

from

Chapter 1 / Lesson 16
28K

Understand the definition of polar coordinates, discover the formula for expressing polar coordinates, and learn how to convert cartesian coordinates into polar coordinates with examples.


Related to this Question

Explore our homework questions and answers library