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r = -6 sinθ Part I: Multiply both sides of this equation by r and use the fact that to rewrite this equation in terms of x and y. I got x^2 + y^2 = -6y Part II: Complete the square to produce the final equation. Part III: Using only your answer to part II, what shape does this graph make?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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So you want to move 6y over to the left side to obtain: x^2 + y^2 + 6y = 0 Then complete the square for the y variables. To do this, you'd take 6, divide it by 2, then square the result. You should end up with 9. |dw:1359140495765:dw|
I don't completely understand. What is the final equation? x^2 + (y+3)^2 - 9?
which seems to simplify to x^2 + y^2

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No, you simply completed the square. There is no way to simplify it to x^2 + y^2. However, if you remember, your equation is now equal to 0. x^2 + (y + 3)^2 - 9 = 0 Add 9 to both sides and see if you recognize this type of equation.
looks like a circle with the origin at -3
and radius of 3
Right. A circle centered at (0, -3) with radius 3. And that's all there is to it :)
Right, Thanks!

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