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Section 9.6 : Polar Coordinates

7. Convert the following equation into an equation in terms of Cartesian coordinates.

6r3sinθ=4cosθ6r3sinθ=4cosθ Show Solution

There 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=4rrcosθ6r3(rsinθ)=4rrcosθ6r4sinθ=4rrcosθ6r3(rsinθ)=4rrcosθ

We can now use the following formulas to finish this problem.

x=rcosθy=rsinθr=x2+y2x=rcosθy=rsinθr=x2+y2

Here is the answer for this problem,

6y[x2+y2]3=4x2+y2x6y[x2+y2]3=4x2+y2x