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Unformatted text preview: qazi (kaq87) HW02 berg (55290) 1 This printout should have 19 questions. Multiplechoice 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.
 Spring '07
 Gilbert
 Multivariable Calculus, Polar Coordinates

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