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Converting Polar to Cartesian Coordinates

  • #1
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).
 

Answers and Replies

  • #2
167
1
Tip: Square x and y and try to add them. Then try to subtitue θ.
 
  • #3
I ended up getting the equation for a circle in the cartesian coordinates which does not match the graph for the polar equation.
 
  • #4
167
1
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...
 
  • #5
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?
 
  • #6
167
1
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.
 
  • #7
I took x2+y2=r2

Because of the r2, the 4sin22θ cancelled out, leaving me with what I got.
 
  • #8
167
1
Your final equation should only contain x's and y's.

x2+y2=4sin2(2θ) right? Subtitue θ and you are done...
 
  • #9
What do I substitute theta with?
 

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