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Unformatted text preview: MATH 114 Name:
04. 25. 2007 EXAM III
Please circle the name of your TA:
Nathan Panike Keya Zhu 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 results that are correct
and relevant to the problem. Please write your answers neatly. Good luck! 1. a) (5 points) Verify the identity 2 sinacos b = sin(a + b) —i— sin(a — b) b) (5 points) Evaluate the following and simplify your answer sin 45° cos 15° = [\D  2. (10 points) Let f :2 2cos(233 + 7?). Determine the following if none write. ” none “: Domain of f amplitude period 1 vertical asymptotes y— intercept Sketch the graph of f (3:). Label all intercepts. 3. (10 points) A ﬂagpole is mounted on a top of a building. The angle of elevation
from a point 100 ft from the base of the building to the top of the ﬂagpole is
60°. The angle of elevation from the same point to the base of the ﬂagpole is
45°. Find the height of the ﬂagpole. V For each of the following questions circle only one answer. If you circle more
than one answer you are not getting any credit, even if the right one was among
your choices. Each problem is worth 4 points. 4. Find the point (x, y) on the unit circle that corresponds to the real number 1771'
9*——6—
x/E 1 1 x/E’S \/§ 1 1 \/§
A.(—2 ,2) B. (—5,?) C. (———2—,§) D. (3—?) E. noneofthese 5. Evaluate cos (arcsin f3" 1 '1 77
A.— B. — C. —5 D. ~E 2 2 E. none of these ' 6. Find all solutions in the interval [0, 27r) of the equation sec4 :1: — 2 sec‘ :3 tan2 x + tan4 :1': = tan2 :1: 37r 57r "7T 7r 57r
~4— D. 21,—;— E. noneofthese 7. In AABC’ we have b = 5, c = 3 and or = 60°. Determine a A.a=19 B. a==49 C. a=34—\/§ D. a=34 E. noneofthese THERE IS A QUESTION ON THE NEXT PAGE!!! 31 '8. Which of the following statements is/are true: 577 P: «é—=150° Q: csc¢=sin1:c
R: cos (cos‘1 = S: 'cos75° = W
A. all statements are true B. P and S only
C. P, Q and 8 only D. P, R and S only E. n0ne of these
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This note was uploaded on 08/08/2008 for the course MATH 114 taught by Professor Nanciu during the Fall '07 term at Wisconsin.
 Fall '07
 NANCIU
 Algebra, Trigonometry

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