m2203sp04exam2solutions

m2203sp04exam2solutions - S. F. Ellermeyer MATH 2203 - Exam...

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February 16, 2004 S. F. Ellermeyer Name Instructions. This exam contains seven problems, but only six of them will be graded. You maychooseanys ixtodo .P leasewr iteDON ’TGRADEontheonethatyoudon ’twantme to grade. In writing your solution to each problem, include su cient detail and use correct notation. (For instance, don’t forget to write “ = ” when you mean to say that two things are equal.) Your method of solving the problem should be clear to the reader (me). If I have to struggle to understand what you have written, then you might not get full credit for your solution even if you get a correct answer. 1. Make sure to show all details of your computations here. You may express angles in terms of radians or degrees (whichever you choose) and you may approximate angles by rounding to two decimal places. (a) Find cylindrical coordinates for the point whose rectangular coordinates are ( x, y, z )= ( 4 , 8 , 2) . Solution: r = p x 2 + y 2 = q ( 4) 2 +(8) 2 = 80 = 4 5 . Also, tan ( θ )= y/x = 2 and θ is in the second quadrant of the xy plane, so θ = arctan ( 2) + π 2 . 0344 116 . 56 . Cylindrical coordinates of this point are thus ( r, θ ,z )= ³ 4 5 , arctan ( 2) + π 116 . 56 , 2 ´ . Let us check our answer: x = r cos ( θ ) =4 5 cos (arctan ( 2) + π ) = 4 5 cos (arctan ( 2)) = 4 5 μ 1 5 = 4 and y = r sin ( θ ) =4 5 sin (arctan ( 2) + π ) = 4 5 sin (arctan ( 2)) = 4 5 μ 2
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m2203sp04exam2solutions - S. F. Ellermeyer MATH 2203 - Exam...

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