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Math151Quiz5Sols

# Math151Quiz5Sols - QUIZ 5(CHAPTER 13 SOLUTIONS MATH 151...

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QUIZ 5 (CHAPTER 13) SOLUTIONS MATH 151 – SPRING 2004 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes, books, or calculators allowed. When graphing, be reasonably accurate, and clearly indicate orientation. Use as many arrowheads as appropriate. Clearly indicate x - and y -intercepts, endpoints, and extreme points when feasible. 1) A plane curve C is described by: x t y t t = + = - £ < 8 2 6 4 0 2 cos sin p Find a corresponding rectangular equation in x and y . (7 points) x t t x y t t y = + fi = - = - fi = + 8 2 2 8 6 4 4 6 cos cos sin sin Use a Pythagorean identity: cos sin 2 2 1 t t + = - Ê Ë Á ˆ ¯ ˜ + + Ê Ë Á ˆ ¯ ˜ = x y 2 8 4 6 1 2 2 Note: C is an ellipse centered at (2, -4) oriented counterclockwise.

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2) A plane curve C is described by: x t y t t = - = + £ £ 2 4 2 0 sin sin p Sketch the graph of C using the grid below. Use arrowheads and labels to clearly indicate orientation for any relevant value of t . (10 points) Eliminate the parameter: y t y t y x x y = + = - - ( ) = - + = 4 2 4 2 4 4 sin sin (line) What part of the line do we pick up for C ? What about orientation?
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Math151Quiz5Sols - QUIZ 5(CHAPTER 13 SOLUTIONS MATH 151...

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