HW02-solutions - qazi (kaq87) HW02 berg (55290) 1 This...

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Unformatted text preview: qazi (kaq87) HW02 berg (55290) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Locate the points given in polar coordinates by P parenleftBig 1 , 1 2 parenrightBig Q parenleftBig 2 , 1 3 parenrightBig , R parenleftBig 4 , 2 3 parenrightBig , among 2 4- 2- 4 2 4- 2- 4 b u b c r u t r s 1. b u t b c P : Q : R : 2. b u t b c P : Q : R : 3. b u t b c P : Q : R : correct 4. b u t b c P : Q : R : 5. b u t b c P : Q : R : 6. b u t b c P : Q : R : Explanation: To convert from polar coordinates to Carte- sian coordinates we use x = r cos , y = r sin . For then the points P parenleftBig 1 , 1 2 parenrightBig Q parenleftBig 2 , 1 3 parenrightBig , R parenleftBig 4 , 2 3 parenrightBig , correspond to b u t b c P : Q : R : in Cartesian coordinates. keywords: polar coordinates, Cartesian coor- dinates, change of coordinates, 002 10.0 points Find the Cartesian coordinates, ( a, b ), of the point given in polar coordinates by P (6 , / 3). 1. ( a, b ) = (6 , 6 3) 2. ( a, b ) = (- 3 , 3 3) 3. ( a, b ) = (- 6 , 3 3) 4. ( a, b ) = (3 , 3 3) correct 5. ( a, b ) = (3 3 ,- 3) 6. ( a, b ) = (3 3 , 3) 7. ( a, b ) = (3 ,- 6) 8. ( a, b ) = (6 3 , 6) Explanation: Since the relationship between Cartesian coordinates and polar coordinates is x = r cos , y = r sin , the point P (6 , / 3) is given in Cartesian co- ordinates by P (6 , / 3) = parenleftBig 6 cos 3 , 6 sin 3 parenrightBig = (3 , 3 3) . keywords: polar coordinates, Cartesian coor- dinates qazi (kaq87) HW02 berg (55290) 2 003 10.0 points Find a polar equation for the curve given by the Cartesian equation y = 3 x 2 . 1. r = 3 csc tan 2. r = 3 sec tan 3. 3 r = sec cot 4. r = 3 csc cot 5. 3 r = sec tan correct 6. 3 r = csc cot Explanation: We have to substitute for x, y in y = 3 x 2 using the relations x = r cos , y = r sin . In this case the Cartesian equation becomes r sin = 3 r 2 cos 2 . Consequently, the polar form of the equation is 3 r = sec tan . 004 10.0 points Which one of the following is the graph of the polar function r = 2 sin( / 2) ? 1. 2. 3. correct 4. 5. qazi (kaq87) HW02 berg (55290) 3 6. Explanation: To determine the polar graph of r = 2 sin( / 2) , look first at its Cartesian graph 2 3 4 1 2- 1- 2 r Then, by tracing in polar coordinates the value of r as varies, looking especially at the values of where r = 0 and the values of r at = 0 , , 2 , 3 , 4 , we obtain the polar graph keywords: polar function, polar graph, sin function, cos function, 005 10.0 points Which one of the following polar functions has graph 1. r = cos 2 2. r = sin 2 3. r = cos 4 4. r = sin 3 correct 5. r = sin 4 6. r = cos 3 Explanation: The graphs of r = sin , r = cos are circles passing through the origin. Thisare circles passing through the origin....
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This note was uploaded on 03/28/2012 for the course M 408 M taught by Professor Gilbert during the Spring '07 term at University of Texas at Austin.

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HW02-solutions - qazi (kaq87) HW02 berg (55290) 1 This...

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