quiz3-8.40-soln. - Combining all these, y & 2cos &...

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MATH 101-B Fall 2004 Quiz 3 ( 8:40-10:30 Group) Oct. 15, 2004 Time: 15 minutes Name: Student No: Follow the directions. No work No credit!! Problem (5 ± 2 ± 3 pts.) a. The graph of a trigonometric function y f x ± is shown in the figure. Find a possible formula for f x ± . Make sure you explain your answer. (The lines y 1, y 1 and y 3 are drawn to help you understand the picture better) 18 16 14 12 10 8 6 4 2 0 -2 -4 5 4 3 2 1 0 -1 -2 x y Solution. Since the function is not equal to 0 at x 0, it could be cos function. Its period is 8 rather than 2 , which is the period of cos x . Note that y cos x 4 ± has period 8. The amplitude of the picture is 2. Finally, the role of the x axis ( y 0 line) for y cos x 4 ± is played by y 1 line in this picture, which indicates that there may be a 1 unit upward shift.
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Unformatted text preview: Combining all these, y & 2cos & & x 4 ± ± 1 is a possible equation for the graph. b. Solve the equation tan x & 3 . Solution. Since tan x is periodic (with period & ) there are infinitely many solutions, which are: x & arctan 3 ± k & & & 3 ± k & , where k is any integer. c. Decide whether the following are equal to sin & 12 or negative of it. Give your reasoning for both answers. sin & & 12 cos 7 & 12 Solution. sin & & 12 & & sin & 12 ,sincesin x is an odd function. cos 7 & 12 & cos & & & 12 & & 2 ± & sin & & & 12 ± & & sin & 12 & usesin x & cos & x & & 2 ±±...
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This note was uploaded on 03/24/2012 for the course MATHEMATIC 101 taught by Professor Many during the Spring '10 term at Sabancı University.

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