Converting a polar equation to an x,y equation

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SUMMARY

The discussion focuses on converting the polar equation r = (1/(2 + cos(θ)) into Cartesian coordinates. Key equations used include r = sqrt(x² + y²), rcos(θ) = x, and rsin(θ) = y. The initial approach involves multiplying both sides by (2 + cos(θ)) and then by r to eliminate the fraction. This method leads to a clearer path for deriving the Cartesian form of the equation.

PREREQUISITES
  • Understanding of polar coordinates and their conversion to Cartesian coordinates
  • Familiarity with trigonometric functions, specifically cosine
  • Knowledge of algebraic manipulation techniques
  • Basic understanding of the relationship between r, x, and y in polar coordinates
NEXT STEPS
  • Practice converting various polar equations to Cartesian form
  • Study the implications of trigonometric identities in polar to Cartesian transformations
  • Explore graphical representations of polar equations
  • Learn about the applications of polar coordinates in real-world scenarios
USEFUL FOR

Students studying mathematics, particularly those focusing on calculus and coordinate geometry, as well as educators teaching these concepts.

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Homework Statement


r=(1/(2+cos(θ))

Homework Equations


r=sqrt(x^2+y^2)
rcosθ=x
rsinθ=y

The Attempt at a Solution



Not sure what first step to take. This problem looks so simple, but I can't seem to get far on paper. Not sure if I should multiply both sides by 2+cos and then multiply both sides by r, or if I should change the fraction as (2+cos)^-1.
 
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Timebomb3750 said:

Homework Statement


r=(1/(2+cos(θ))


Homework Equations


r=sqrt(x^2+y^2)
rcosθ=x
rsinθ=y

The Attempt at a Solution



Not sure what first step to take. This problem looks so simple, but I can't seem to get far on paper. Not sure if I should multiply both sides by 2+cos and then multiply both sides by r, or if I should change the fraction as (2+cos)^-1.
You knew the answer all along.
 

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