Mid 2 Solutions - MATH 3 ' ' MIDTERM 2 05/20/2011...

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Unformatted text preview: MATH 3 ' ' MIDTERM 2 05/20/2011 Instructor: Nandini Bhattacharya Use of books, notes and graphing utilities is not permitted in this exam. ' You must show all your work to get partial credit. Your Name Your TA & Section time ------------------------------- —-.- --------- -- Max possible Your score Problem 1: 15 3—H w’ Problem 2: I 10 “- Chm/15“ Problem 3: 15 PM Problem 4: 10 Cl/Vfif: Problem 5: 15 (MS Problem 6: 10 Dad," M Problem 7: 1o RBWK I Problem 8: 15 Remix {:1 TOTAL . 15 oi ts) Let 6 be an angle in standard position between 0-and 21: such that 31116 = — and (3050 > 0 . Flrst draw a plcture of 6. In what quadrant IS 6 ? _ Then find th' act value 0 3 3.) cos 9 = F.“ S ‘ e) cch— 7—” Em W . , .g t) since) : 4249\"1461; 2. (10 points) Find the exact values of the six trigonometric functions of the given angle. .If any are nOt defined ‘ “not defined.” ' . : ' Siv‘fi chef}- #9 r t 6+0 t9 ~—- ———.~" (5—9” 1“ a) “:1 Awg dense + 53mg {125% sec 6 030 9 4. (10 points) You want to invest $710,000 for 5 years, and you have a choice between two accounts. The first pay 6% per annum compounded annually . The second pays 5% per annum compounded continuously. Whic ._ the eter _u,- 1 ‘7 r I1! I S A = P[l + 7‘) : Money invested n-times a year,- I 1’! A = Pe”: Money invested continuously 5. (15 points) A segment of a circleis' a region bounded by "an arc of the circle and its chord. Compute the area of the segment (the shaded region) in the figure below. Express your answer in exact form in terms of the constant 71'. ' Li) 6. (10 points) You know the rate of rotation of a wheel as 6 revolutions/sec. You also know the radius of this Wheel, r = 12 cm . Find the folloWing: ' a) The angular speed, in units of radians/minute; . ' b) The linear speed in Gin/minute, of a halfway between the center of the wheel and the 7. (10 points) A ladder 18 ft long leans against a building. “ 600 with the ground. a) How high up the side of the building does the ladder reach? Give an exact answer. A b) Find the horizontal distanee from the foot of the ladder to the base of the building. Ski's-«3‘0 : A; film/~30! mg g 4 \) _ :- 4 3:. at .55 l .3 gown?» i 1 _ 8. (15 points) Consider the function the function _ (x) = cos 2x —- 4* +1} Find the . , ‘ m C w I I ma.) 8= 2., 7"" .. following: a) (2 points) The amplitude off. @ , b) ‘ (3 points) The period of f. A“ I E: c) (3 points) The horizontal phase shift of f. ...
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This note was uploaded on 08/09/2011 for the course MATH 3 taught by Professor Staff during the Spring '08 term at University of California, Santa Cruz.

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Mid 2 Solutions - MATH 3 ' ' MIDTERM 2 05/20/2011...

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