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
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View this answerFirst, we will substitute {eq}\sin(\theta) = \displaystyle \frac{y}{r} {/eq} and rewrite the equation accordingly:
{eq}\begin{align*} \displaystyle...
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Chapter 1 / Lesson 16Understand the definition of polar coordinates, discover the formula for expressing polar coordinates, and learn how to convert cartesian coordinates into polar coordinates with examples.