My Calculus 2 instructor was out (coaching), and gave us the questions 57,59,61. I have inserted the questions, the book answers and my work on 57,59. I haven't inserted 61 as I am getting the wrong answers. Thanks so much for whatever help you can give me.

=3cose + y= (3+ 3 ( /2) (532 ) 57 45 , (4= - 953 /4 1 x = ( = 3 sin Ocos e) - (3+lose [ sin 0)= 0 X =6 X = -F - 314 3 - 1.5 3 + 3 ( 42 ) ( 12 ) - 3 - (3+ 3cosb) ( Lose 4 59r= 2 cos 20 2 CosJz u = (@ cos 20 * sine ) X - (2 cos20) (cose) dy - 4 since ( sing ) + (2cos20) ((oso ) ax ( - 4 sin 20 YEOSD) - ( Rcos 20( Sing) - HeinzB sina + 2 cos 20 cosa = Q y = 2 4 = - 2 - 4sin 20 cost - (x 509 20 Sing - 2 sIn20 cose - cos 20 sino = D Y - 2 X = - 2( 55. Exploring Using Technology Graph r, = 3 - 2 cos . Clear the screen and graph ry = 3 + 2 cos 0. Clear the screen and graph 13 = 3 + 2 sin 0. Clear the screen and graph ra = 3 - 2 sind Describe the pattern. 56. Horizontal and Vertical Tangent Lines Find the horizontal and vertical tangent lines of the cardioid r = 1 - sing 57. Horizontal and Vertical Tangent Lines Find the horizontal and vertical tangent lines of the cardioid r = 3+ 3 cos9.scale and veruca 2 cos @ discussed in Example 3. CAS 59. Horizontal and Vertical Tangent Lines Find the boring and vertical tangent lines of the rose with four petals r = 2 cos(20), 0