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

TL;DR

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

Key Insights

• 🐻‍❄️ The process of converting a polar equation to a Cartesian equation requires understanding the trigonometric representation of sin(θ) and cos(θ).
• 🆘 Multiplying the equation by R helps eliminate fractions and simplify the equation.
• 👻 Completing the square allows us to recognize the equation as that of a circle.

Transcript

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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.