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 stepbystep process.
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.