Combining 2 Equations into 1 Polar Equation

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SUMMARY

The discussion focuses on combining two polar equations, specifically x(θ) = a*cos(θ) * sin(k*θ) and y(θ) = a*sin(θ) * sin(k*θ), into a single polar equation. The key method suggested is to square both equations and sum them to derive the radius r, using the formula r² = x² + y². This approach simplifies the representation of the equations in polar coordinates, providing a unified expression for r.

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  • Understanding of polar coordinates and their equations
  • Familiarity with trigonometric identities
  • Basic knowledge of algebraic manipulation
  • Experience with mathematical functions and graphing
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  • Research the derivation of polar equations from Cartesian coordinates
  • Learn about trigonometric identities relevant to polar equations
  • Explore the implications of squaring equations in mathematical analysis
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Mathematicians, physics students, and anyone interested in advanced algebra and polar coordinate systems will benefit from this discussion.

jfhatch
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If I have 2 equations as shown below, how can I make them into 1 polar equation?

x(theta) = a*cos(theta) * sin(k*theta)
y(theta) = a * sin(theta) * sin(k*theta)

Thanks very much
 
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r = radius from x and y:

[tex]r^2 = x^2 + y^2[/tex]
 
To maybe add a little to out's hint, square both of the equations you have and add them together. See what happens :).
 

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