# HW02-solutions - sagbini (ces3287) – HW02 – berg –...

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Unformatted text preview: sagbini (ces3287) – HW02 – berg – (55811) 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 2 , 2 3 π parenrightBig , Q parenleftBig 1 , 1 2 π parenrightBig R parenleftBig 2 , 1 3 π 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 θ , y = r sin θ . For then the points P parenleftBig 2 , 2 3 π parenrightBig , Q parenleftBig 1 , 1 2 π parenrightBig R parenleftBig 2 , 1 3 π 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 (2 , π/ 3). 1. ( a, b ) = (1 , 1 √ 3) correct 2. ( a, b ) = (2 , 2 √ 3) 3. ( a, b ) = (- 2 , 1 √ 3) 4. ( a, b ) = (1 √ 3 , 1) 5. ( a, b ) = (2 √ 3 , 2) 6. ( a, b ) = (- 1 , 1 √ 3) 7. ( a, b ) = (1 √ 3 ,- 1) 8. ( a, b ) = (1 ,- 2) Explanation: Since the relationship between Cartesian coordinates and polar coordinates is x = r cos θ , y = r sin θ , the point P (2 , π/ 3) is given in Cartesian co- ordinates by P (2 , π/ 3) = parenleftBig 2 cos π 3 , 2 sin π 3 parenrightBig = (1 , 1 √ 3) . keywords: polar coordinates, Cartesian coor- dinates sagbini (ces3287) – HW02 – berg – (55811) 2 003 10.0 points Find a polar equation for the curve given by the Cartesian equation y 2 = 3 x . 1. 3 r = sec θ cot θ 2. r = 3 csc θ cot θ correct 3. 3 r = csc θ cot θ 4. 3 r = sec θ tan θ 5. r = 3 sec θ tan θ 6. r = 3 csc θ tan θ Explanation: We have to substitute for x, y in y 2 = 3 x using the relations x = r cos θ , y = r sin θ . In this case the Cartesian equation becomes r 2 sin 2 θ = 3 r cos θ . Consequently, the polar form of the equation is r = 3 csc θ cot θ . 004 10.0 points Which one of the following is the graph of the polar function r = 1- 2 sin(2 θ ) ? 1. 2. 3. 4. correct 5. sagbini (ces3287) – HW02 – berg – (55811) 3 6. Explanation: To determine the polar graph of r = 1- 2 sin(2 θ ) , look first at its Cartesian graph π 2 π 3 π 2 2 π 3 2 1- 1 r θ Then, by tracing in polar coordinates the value of r as θ varies, looking especially at the values of θ where r = 0 and the values of r at θ = 0 , π 2 , π , 3 π 2 , 2 π , 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 3 θ correct 2. r = sin 2 θ 3. r = cos 4 θ 4. r = sin 4 θ 5. r = cos 2 θ 6. r = sin 3 θ Explanation: The graphs of r = sin θ , r = cos θ are circles passing through the origin. Thisare circles passing through the origin....
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## This note was uploaded on 04/15/2011 for the course MATHEMATIC 103M taught by Professor Berg during the Spring '11 term at University of Texas at Austin.

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HW02-solutions - sagbini (ces3287) – HW02 – berg –...

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