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.

Transcript

let's convert this polar equation into a cartisan equation here we have R = to 6 sin Theta minus 2 cosine Theta these are the things that we have to know and remember and these are the things that we have to use as you can see we have sin Theta cosine Theta right here and we can plug in these two things into here and here let's do that first so we ... Read More

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.

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.