solution_pdf-1 - gonzales(pag757 HW 07 Odell(57000 This...

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gonzales (pag757) – HW 07 – Odell – (57000) 1 This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Locate the points given in polar coordinates by P p 2 , 2 3 π P , Q p - 3 , 1 2 π P R p 2 , 1 3 π P , 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 : 4. b u t b c P : Q : R : 5. b u t b c P : Q : R : correct 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 . ±or then the points P p 2 , 2 3 π P , Q p - 3 , 1 2 π P R p 2 , 1 3 π P , 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 Which, iF any, oF A. ( - 4 , 4 π/ 3) , B. (4 , π/ 3) , C. (4 , 13 6) , are polar coordinates For the point given in Cartesian coordinates by P (2 , 2 3)? 1. A and B only correct 2. A only 3. C only 4. B and C only 5. A and C only 6. B only 7. all oF them 8. none oF them Explanation: To convert From Cartesian coordinates to polar coordinates we use the relations: x = r cos θ , y = r sin θ , so that r 2 = x 2 + y 2 , tan θ = y x . ±or the point P (2 , 2 3) in Cartesian co- ordinates, thereFore, one choice oF r and θ is
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gonzales (pag757) – HW 07 – Odell – (57000) 2 r = 4 and θ = π/ 3, but there are equivalent solutions for r < 0 as well as values of θ dif- fering by integer multiples of π . For the given choices we thus see that A. TRUE: - 4 cos(4 3) = 2 , - 4 sin(4 3) = 2 3 . B. TRUE: solution noted already. C. FALSE: di±ers from 6 by 2 π . 003 10.0 points A point P is given in Cartesian coordinates by P ( - 1 , 1). Find polar coordinates ( r, θ ) of this point with r < 0 and 0 θ < 2 π . 1. p - 3 , 3 π 4 P 2. p - 3 , 7 π 4 P 3. p - 2 , 5 π 4 P 4. p - 2 , 3 π 4 P 5. p - 2 , 7 π 4 P correct 6. p - 3 , 5 π 4 P Explanation: Since the relationship between Cartesian coordinates and polar coordinates is x = r cos θ , y = r sin θ , the point P ( - 1 , 1) in Cartesian coordinates can be given in polar coordinates as P p - 2 , 7 π 4 P , 004 10.0 points Which one of the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 3 r 4 , 1 12 π θ 2 3 π ? 1. 2 4 2. 2 4 3. 2 4 4. 2 4 5. 2 4 6. 2 4 correct
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gonzales (pag757) – HW 07 – Odell – (57000) 3 Explanation: Using the defnition oF polar coordinates ( r, θ ), we see that the region defned by the inequalities 3 r 4 , 1 12 π θ 2 3 π is 2 4 keywords: polar coordinates, inequalities, po- lar graph, 005 10.0 points ±ind a polar equation For the curve given by the Cartesian equation 3 y 2 = x . 1. 3 r = csc θ cot θ correct 2. 3 r = sec θ tan θ 3. r = 3 sec θ tan θ 4. r = 3 csc θ tan θ 5. 3 r = sec θ cot θ 6. r = 3 csc θ cot θ Explanation: We have to substitute For x, y in 3 y 2 = x using the relations x = r cos θ , y = r sin θ .
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solution_pdf-1 - gonzales(pag757 HW 07 Odell(57000 This...

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