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# Consider the polar curve r = 2 + sin(3theta). Determine the Cartesian equation (in slope-intercept form) of the line tangent to the curve at the Cartesian point (2,0). (?)

## First of all, the wording of the problem has me very confused. I don't know exactly what I'm supposed to find; y? or dy/dx ? But I gave it a go and this is what I got: I used sin(3theta) = 3sin(theta) - 4sin^3(theta) to get r = 2 + 3sin(theta) - 4sin^3(theta) then, I multiplied both sides by r r^2 = 2r + 3rsin(theta) - 4rsin^3(theta) I substituted using the formulas x = rcos(theta), y = rain(theta), & r^2 = x^2 +y^2 to get: x^2 + y^2 = 2r + 3y - 4ysin^2(theta) From here, I have no idea what to do with the monster I created. Could you please point out my error(s) and show the correct solution for me? (ps. the question mark had to be in there otherwise i couldn't post it because "it wasn't a question")

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