Here are Calculus problem:

(Parametric Equations and Polar Coordinates) 3. Converting between Polar and Cartesian systems: (a) The polar equation r = 6sin(0) gives the graph of a circle. Rewrite this polar equation in Cartesian (ry) form. Then use completing the square to determine the radius and center of this circle. (b) Write a polar equation for the curve described by the Cartesian equation y = 2. Write your answer in the form r = f(0). (c) Convert the point with Polar representation (r, 0) = (2, ) to Cartesian coordinates. (d) Convert the point with Cartesian representation (x, y) = (-1, v3) to Polar coordinates. (e) Multiple representations: Write the polar point (2, " ) in four other ways: (i) r > 0, 0 > 0; (ii) r > 0, 0 0; (iv)r