Pre-Calc Homework Solutions 425

Pre-Calc Homework Solutions 425 - Section 10.5 61. If (r, )...

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61. If ( r , u ) is a solution, so is ( r , p 2 u ). Therefore, the curve is symmetric about the y -axis. The curve does not have x -axis or origin symmetry. 62. If ( r , u ) is a solution, so is ( 2 r , u ). Therefore, the curve is symmetric about the origin. And if ( r , u ) is a solution, so is ( r , 2 u ). Therefore, the curve is symmetric about the x -axis. And since any curve with x -axis and origin symmetry also has y -axis symmetry, the curve is symmetric about the y -axis. 63. (a) Because r 5 a sec u is equivalent to r cos u 5 a, which is equivalent to the Cartesian equation x 5 a . (b) r 5 a csc u is equivalent to y 5 a . 64. (a) The graph is the same for n 5 2 and n 52 2, and in general, it’s the same for n 5 2 k and n 52 2 k . The graphs for n 5 2, 4, and 6 are roses with 4, 8, and 12 “petals” respectively. The graphs for n 56 2 and n 56 6 are shown below. n 56 2 [ 2 3, 3] by [ 2 2, 2] n 56 6 [ 2 3, 3] by [ 2 2, 2] (b) 2 p (c) The graph is a rose with 2 ) n ) “petals”. (d)
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