Convert a polar equation to a cartesian equation: circle! | Summary and Q&A

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April 23, 2016
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blackpenredpen
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Convert a polar equation to a cartesian equation: circle!

TL;DR

Learn how to convert a polar equation to a Cartesian equation by following a step-by-step process.

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Questions & Answers

Q: What is the first step in converting a polar equation to a Cartesian equation?

The first step is to substitute sin(θ) and cos(θ) with y/R and x/R, respectively, in the equation.

Q: How can fractions be eliminated from the equation?

By multiplying the entire equation by R, the fractions involving y/R and x/R can be eliminated.

Q: What is the purpose of completing the square in the Cartesian equation?

Completing the square allows us to identify the equation as that of a circle in Cartesian coordinates.

Q: How can the center and radius of the circle be determined?

By analyzing the completed square form of the equation, the center of the circle can be identified as (-1, 3), and the square root of 10 represents the radius.

Summary & Key Takeaways

  • The first step in converting a polar equation to a Cartesian equation is to substitute sin(θ) and cos(θ) with their respective Cartesian forms (y/R and x/R).

  • To eliminate fractions, multiply the entire equation by R.

  • Simplify by replacing R^2 with x^2 + y^2.

  • Move terms to one side to complete the square and identify the equation as a circle in Cartesian coordinates.

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