In Problems 3840, give inequalities for r and _ that describe the following regions in polar coordinates. (a) Make a table of values for the equation r = 1_sin _. Include _ = 0, _/3, _/2, 2_/3, _, . (b) Use the table to graph the equation r = 1 _ sin _ in the xy-plane. This curve is called a cardioid. (c) At what point(s) does the cardioid r = 1 _ sin _ intersect a circle of radius 1/2 centered at the origin? (d) Graph the curve r = 1 _ sin 2_ in the xy-plane. Compare this graph to the cardioid r = 1 _ sin _.
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