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114-nenciu-07faex03 - MATH 114 Name 11 30 2007 EXAM III...

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Unformatted text preview: MATH 114 - Name: 11. 30. 2007 EXAM III Please circle the name of your TA: Lino Amorim Ali Godjali Alec Johnson Sarah Matz - Kim Schattner Show all your work in order to receive credit. A‘ correct answer without any work . will receive 0 credit. Partial credit will be given ONLY for work that is correct and relevant to the problem. Please write your answers neatly. Please make sure your cell phones areiturned OFF! Good luck! -— --_ -_ -_ 1. Let 6 be an angle in Quadrant IV. If sin0 = ——2— determine the following; '\/§ (Simplify your answers and rationalize the denominat0r(s) of your answers) a) (4 pts) cos6 b) (3 pts) sin 20 c) (3 pts)‘tan («9 — g) i 2. (lO'points) Let f (x) = —2sin (g — g). Determine'the following (if none write “none”). ' ' Domain of f (:13) l . . V Range of f(a:) amplitude ‘ period , phase shift y—intercept vertical asymptotes ‘ horizontal asymptotes Sketch two periods of the graph of f (33). Label all art—intercepts and y—intercepts. 3. a) (5 points) Find the area of a regular hexagon inscribed in a circle of radius 4 in. (A regular hexagon is a polygon with six sides. of equal length). l I :5), (5 points), 'Vefify: the identlt'y‘ V : 1 1 . 2 ———-—-+——————=2(:sc so 1—cosx 1+cosx For each of the following questions circle only one answer. If you circle more than one answer you will not get any credit even if the right one was among your choices. There are 5 problems and each problem is worth 4 points. 6 1/1 . 3 0, sin6 < 0, and 0 g 0 < 27r, determine sin (5) 10 A fl 10+3x/10 B . 10mm c. 10—3§/fi ‘ ' 20 ‘ ‘ 20 ' 2o . D. ——‘/ 1042????- E. none of these 5. ‘Which of the following is a vertical asymptote to the graph of y = tan (2a: — 3;.) 4. Given that *cos6 = A. 3’ = -—- ~ 13- $7—‘-—*- C $=— . D.. a: = g , .- E..,-none 'ofvtheSe.-.-1 ,. . . l .9: 5m 4sin6 7r57r 7r37r57r77r 7r27r ,4vr57r' .———— —-——-——— —— D. —— E. fh A6,6 B 4,4,4,4 C 3,3 3,3 noneotese 7. Given a triangle ABC with a = 105°, fl = 30°, and b : 5, find 0. A. 5\/§ B. E? C. 10\/§ D. E. none of these 5V5 2 THERE IS A PROBLEM ON THE NEXT PAGE!!! 8. Which Of the fellowing statements is/ are true? 77r o ‘ ' _ 77r P. -1—2——105 R. (308(12) <0 Q: sin‘1 (sin %) = f—ig S: cscfc : (sinx)“1 A. an statements are true B. P, Q, R only C. P, R only D. P, R, S only V E. none of these ~ 9. BONUS QUESTION (2 points) 7 3143.14159265) =,;_,‘_ . , A. —1 B. 0 C. 1 D. \/§ E. none ofthese ...
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