Converting Polar to Cartesian Coordinates

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Homework Help Overview

The problem involves converting the polar equation r=2sin(2(θ)) into Cartesian coordinates. Participants are discussing their understanding of the conversion process and the resulting equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to express the polar coordinates in Cartesian form using the relationships x=rsin(θ) and y=rcos(θ). Some are exploring the implications of squaring x and y and adding them together. Others are questioning the validity of their results, particularly regarding the shape of the graph represented by the Cartesian equation.

Discussion Status

The discussion is ongoing, with participants offering tips and questioning each other's reasoning. There is a recognition of potential mistakes in the conversion process, and some participants are exploring the need for trigonometric substitutions. Multiple interpretations of the results are being discussed.

Contextual Notes

Participants are navigating the complexities of the conversion process, including the implications of their derived equations and the need to ensure that the final result is expressed solely in terms of x and y. There is an emphasis on the relationship between the polar and Cartesian forms and the discrepancies observed in the graphical representations.

tina_081493
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I was given the problem r=2sin(2(θ)). I'm supposed to write the equation in the Cartesian Coordinates. I understand the basics to this but I'm not really sure how I'm supposed to write the equation when I have x=2sin(2(θ))cos(θ) and y=2sin(2θ)sin(θ).
 
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Tip: Square x and y and try to add them. Then try to subtitue θ.
 
I ended up getting the equation for a circle in the cartesian coordinates which does not match the graph for the polar equation.
 
tina_081493 said:
I ended up getting the equation for a circle in the cartesian coordinates which does not match the graph for the polar equation.
Could you write down your final result? I doubt that it is a circle equation...
 
Ok so as I was typing out my work, I realized a mistake I made. So now I'm down to:

(cosθ)^2+(sinθ)^2+2cosθsinθ=1

Am I going to need to use some kind of trig substitution to solve this now?
 
I don't know how did you come up with that :/

If you square x and y, you get respectively: x2=4sin2(2θ)cos2(θ) and y2=4sin2(2θ)sin2(θ).
Now you've got to add the two equations and apply the distributive law to the second part in order to get rid of the cos2(θ)+sin2(θ) terms. It should be straightforward from now on. Your final step is to subtitue θ in the remaining 4sin2(2θ) term.
 
I took x2+y2=r2

Because of the r2, the 4sin22θ canceled out, leaving me with what I got.
 
Your final equation should only contain x's and y's.

x2+y2=4sin2(2θ) right? Subtitue θ and you are done...
 
What do I substitute theta with?
 

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