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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‘éLQTv  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§& ' EmmaE?” 7 ' I e) csc_6= ﬁVx
in ii; if a f) Sln('6) “H‘ mfﬁ‘i 11C" EEK
a ,wrww"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 {MDT391i) {95% a gwxﬁ Sawﬂy
 x5334?) gongi 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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