Converting from Polar to Rectangular

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SUMMARY

The discussion focuses on converting the polar equation r=3/(4cosθ-sinθ) into rectangular form. The correct transformation leads to the equation 4x - y = 3, utilizing the relationships x = rcosθ and y = rsinθ. Participants confirm that eliminating the denominator is the key step in achieving the rectangular representation. The conversion process is straightforward and relies on fundamental polar-to-rectangular coordinate transformations.

PREREQUISITES
  • Understanding of polar coordinates and their relationships to rectangular coordinates.
  • Familiarity with the equations x = rcosθ and y = rsinθ.
  • Knowledge of basic algebraic manipulation to eliminate denominators.
  • Proficiency in using the equation r = √(x² + y²) for conversions.
NEXT STEPS
  • Study the process of converting other polar equations to rectangular form.
  • Explore the implications of polar and rectangular coordinates in calculus.
  • Learn about graphing polar equations and their rectangular counterparts.
  • Investigate advanced applications of polar coordinates in physics and engineering.
USEFUL FOR

Students in mathematics, particularly those studying calculus and coordinate geometry, as well as educators teaching polar coordinate transformations.

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Homework Statement



Convert r=3[tex]/[/tex](4cos[tex]\theta[/tex]-sin[tex]\theta[/tex]) to rectangular form

Homework Equations



r=[tex]\sqrt{}[/tex]x^2+y^2

The Attempt at a Solution



4x-y=3 ?
 
Last edited:
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Relevant equations: x=rcos0, y=rsin0

All you need to do is get rid of the denominator and you're home free.
 
tachu101 said:

Homework Statement



Convert r=3[tex]/[/tex](4cos[tex]\theta[/tex]-sin[tex]\theta[/tex]) to rectangular form

Homework Equations



r=[tex]\sqrt{}[/tex]x^2+y^2

The Attempt at a Solution



4x-y=3 ?
Yes, that's correct.
 

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