is the flower-like graph with 52. The graph of r = cos (30) 10 petals, shown next at the left: у у (1,5) X (-1) 0 (-1,0)

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is the flower-like graph with 52. The graph of r = cos (30) 10 petals, shown next at the left: у у (1,5) X (-1) 0 (-1,0) 0.0) Bat (-1, 2 (-1,3,7 ) = The graph of r = cos (0) 6) is also a flower-like graph, but with 5 petals, shown in the preceding figure at the right. (a) Why does the graph of r = cos Ce) have 10 petals while the graph of r = cos e) has only 5? (b) Let be a positive rational number reduced to low- est terms with p > q. How many petals will the curve (20) have? What is the smallest interval of 9 the form [0, b) required to obtain the graphs of these curves? Explain how to calculate b in terms of p and 9. (c) What is the graph of r = cos ko when k is an irrational 9 r = COS number?