SUMMARY
The Cartesian equation for the polar curve r = 9 cosθ is x² + y² = 9x. The conversion process involves using the relationships rcosθ = x and cosθ = x/r. Initially, the user derived (x - 9/2)² + y² = (9/2)², which was incorrect for the online homework submission due to formatting issues. The correct form simplifies to x² + y² = 9x, which aligns with the expected answer.
PREREQUISITES
- Understanding of polar coordinates and their conversion to Cartesian coordinates.
- Familiarity with trigonometric identities, particularly rcosθ and cosθ.
- Basic algebra skills for manipulating equations.
- Experience with online homework systems and their formatting requirements.
NEXT STEPS
- Study the conversion methods between polar and Cartesian coordinates.
- Learn about the implications of equation formatting in online homework systems.
- Explore additional examples of polar curves and their Cartesian equivalents.
- Practice solving polar equations using software tools like GeoGebra or Desmos.
USEFUL FOR
Students studying mathematics, particularly those focusing on calculus and coordinate geometry, as well as educators looking to enhance their teaching methods for polar and Cartesian equations.
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