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Section 9.6 : Polar Coordinates
7. Convert the following equation into an equation in terms of Cartesian coordinates.
6r3sinθ=4−cosθ6r3sinθ=4−cosθ Show SolutionThere is a variety of ways to work this problem. One way is to first multiply everything by rr and then doing a little rearranging as follows,
6r4sinθ=4r−rcosθ⇒6r3(rsinθ)=4r−rcosθ6r4sinθ=4r−rcosθ⇒6r3(rsinθ)=4r−rcosθWe can now use the following formulas to finish this problem.
x=rcosθy=rsinθr=√x2+y2x=rcosθy=rsinθr=√x2+y2Here is the answer for this problem,
6y[√x2+y2]3=4√x2+y2−x6y[√x2+y2]3=4√x2+y2−x