Calculus III: Worksheet #2 in Polar Coordinates by Professor Broughton (Winter 03-04), Assignments of Mathematics

Download Calculus III: Worksheet #2 in Polar Coordinates by Professor Broughton (Winter 03-04) and more Assignments Mathematics in PDF only on Docsity! MA 113 - Calculus III Worksheet #2 Polar Coordinates Professor Broughton − Winter 03-04 Name: Box #: In this work sheet perform the elementary calculations by hand and then check with Maple 1. Fill in the table below Cartesian Polar (1, 2) ( √ 5, arctan(1 2 )) = (2. 236 1, 0.46365) (3 cos ¡ 3π 4 ¢ , 3 sin ¡ 3π 4 ¢ ) = (−2.1213, 2.1213) (3, 3π 4 ) (−2, 2) (2,−π 4 ) (4.5 cos (0.13) , 4.5 sin (0.13)) = (4.462, 0.58335) (4.5, 0.13) 2. Fill in the table below Cartesian Polar x2 + y2 = y, x2 + ¡ y − 1 2 ¢2 = 1 4 r = sin θ (x− 1)2 + (y − 1)2 = 4 r2 − 2r(sin θ + cos θ)− 2 = 0 r5 = r2 cos2 θ − r2 sin2 θ, (x2 + y2) 5 2 = x2 − y2, r3 = cos(2θ) (x2 + y2) 5 = (x2 − y2)2 x+ y = 1 r(sin θ + cos θ) = 1, r = 1 sin θ+cos θ 3. Sketch the curve in polar coordinates r = 1 + cos θ