please answer from your own work on a paper providing all steps for good feedback.

6. Let's practice converting from one system to another. a] Consider the points with rectangular coordinates (ED). (1,1), {5.51%}, and {EL'3']. Express each ofthese points using polar coordinates. b] Consider the points with polar coordinates ([153). {2.31), (1.1], and {4. will]. Express each of these points using rectangular coordinates. c] Find formulas to express x and j; in terms of r and 3. d] Find formulas to express 1" and d in terms of x and 3;. '3". Sketch the following graphs. a] r=3 b] d=1rf6 c] r=d d} r==lsinII5l 8. Derivatives help reveal the behavior of a polar curve. a] Explain in sentences what the derivatives dxfdf. dyfdf. and drfdd reveal about the graph of a polar function. h] Suppose at a certain point on a polar curve, we have the following. Wl'lat does this reveal about the point? (#230 EWEN} drill] :13 dd :13 c] Express dxfd and dyfd in terms of r. 3.. and drfrt. [You will need the product rule.) d] Express dyfdx in terms of r, d, and drjd. e] For the cardioid r = 1 + sin 3. nd dyfdx and use it to gure out the slope of the tangent line when H = HI 3