Mid 2 (V2) Solutions

Mid 2 (V2) Solutions - i MATH 3 MIDTERM 2 (V2) ' --...

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Unformatted text preview: i MATH 3 MIDTERM 2 (V2) ' -- 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. . r I Your Name ------ “iiifaj 1---‘ _________ __. ____ -1.-- Student id# ...... D Your TA & Section time --------------------- n: .................. -— Max possible Your score Problem 1: 15 ‘ Problem 2: 10 Problem 3: 15 Problem 4: 10 Problem 5: 15 Problem 6: 10 ‘ Problem 7: 10 Problem 8: 15 TOTAL 1. (15 points) Let 6 be an angle in Standard position between 0 and 27: such that 5 . sin9 : E, and cost? < 0 . First draw a picture of 9. In what quadrant IS 9 ? :‘L Sheet 4" Cfi‘éLQT-v - it; Then find the exact valu of the following: / "~-—~- m. r“ ((ea; 2*: m Rig to _ x 3 a i a) cosQ= N in i3 . I _. my c) cote:i f” “*5 d) sec9‘=\::m§& ' Emma-E?” 7 ' I e) csc_6= fiVx in ii; if a f) Sln('6) “H‘- mffi‘i 11C" EEK a ,w-rww-"Mm': : ' “f i r ’ I Qh) 6: Use your calculator 2. (15 points) Find the exact values of the six trigonometric functions of the gixfen angle. If any are not defined, say__“not defineF.” ‘csc6 E“ a) flame *mw‘? . .We :2 939+ COt + [an {MDT-391i) {95% a g-wxfi Sawfly - x5334?) gong-i 00 u 2 Saw? 4. (10 points) You want to invest $10,000 for 4 years, and you have a choice between The first pay 6% per annum compounded annually. The second pays 5% Which is the better investment? l “T two accounts. per annum compounded continuously. n! r A = P£1+ —) : Money invested 'n—times a year, n A = Pe”: Money invested continuously FMWW d by an arc of the circle and its 5. (10 points) A segment of a circle is a region bOunde e below. Express chord. Compute the area of the segment (the shaded region) in the figur Myonnmgfswer in exact form in terms of the constant 71: . m:3m\”m§-EW>§%M ' i 7 ' 6. (10 points) You know the rate of rotation of a wheel as 15 revolutions/sec. You also know the radius of this wheel, r = 20 cm. Find the following: __ Pfiflgflm m.H...a.....__v_h__m_9 ,- ‘— a) The angular speed, in units of radians/sec; b) The linear speed in cm/sec, of a halfway between the center of the wheel and the circumference. {ME/“L. q J at; g‘fi‘h Sith 7. (10 points) A ladder 15 ft long leans against a building. The ladder forms an angle of 300 with the ground. a) How high up the side of the building does the ladder reach? Give an exact answer. ‘ A;_.,;WWMW;WM. a ‘ . . ' \n £11 ' : - “t a _, r. [m a) (2 points) The amplitude of f. b) (3 points) The period of f. ' P '6 f? c) (3 points) The phase shifi: of f. Wis,” g. fl E g} “015?, atwgrem E ___ d) (4 points) The graph of f for at least} periods. { ‘ «m ZN grimy ...
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Mid 2 (V2) Solutions - i MATH 3 MIDTERM 2 (V2) ' --...

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