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Unformatted text preview: Math 113 EXAM I, Feb. 9, 2004, (50 minutes).
NAME: SECTION: Instructor: TO RECEIVE CREDIT FOR AN ANSWER,
YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. I. (20 points)
1) Draw with best possible accuracy an angle 6 in standard position such that( sin 6— — _ Show all the possibilities for the terminal side. 2) Draw with best possible accuracy an angle V with tanz/ II. Convert from degrees to radians and vice versa (keep exact values) (10 points)l IT
0 _ TI“ 2 — Cl.
12 _Q2 x 7,80 rad. IS ’14 12 radians: Q2} l%0\°: (2i Tr 60": 1 III. The circle whose arc is shown on the ﬁgure has a radius of length 6 (units), and O is its center. The measure of the angle 0 = LACB is g radians. IN ALL THIS PROBLEM
KEEP EXACT VALUES. (35 points) 1) Give the value of the angle [A03 in degrees and in radians.
4. 0 BC. :. 4, O C. % 2 “>8 V'a‘\ (Xboch \"V‘\‘wuxh\ . I an
A (013: TV —(“'/y+W/g\= 6—3:: , LAOB:TI‘—1¢°B= Iqrv'oA: 1+3 l 2) Evaluate the length of the line segment AB, and evaluate the area of the triangle 0B0. :: Bl «AI—Lzr
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CAB”M\‘89AWMW°JQ“ ’3‘” lbw—5 “(E—E‘s" m—W‘L \+\)"z' 4) Evaluate cos g, and sin % (exact values!). 0"
\Bc.\°'.—_ \cA\"+ \A (3?; (“3031+ an)‘ =(bc+\s+aeﬁ.)+ v3 23““ 9—5 “but. 6 m1, va‘I \be _ 301 2 ‘ \AU MW? 02”; P ‘ um ‘ mm m w  _.
CM — = M
3 [e c\ 6 Warm, 7 ‘ Comwmm may Aoaavcw 5) Evaluate the length of the arc of circle form D to B. ML \ 1 qu': 9:03—7 . ‘ ‘\ \ \A
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Mleu Rem)»: 6%? ”Lil 6) Evaluate the area of the shaded region. CW‘U» are, I'QaMoXA 08 C : (lg—'2. 0&5on andgAeJI'ELOBD: ‘
“Hr IV. Two villages on the path of a plane are seen at an angle of depression of 50° and
29". The distance between these two villages (at the same altitude) is 5 miles. At which
elevation above the villages is the plane ﬂying? (1 mile 2 5280 ft) Method imposed: Solve
this problem with the tools of Chapter 2 (Right Triangles, deﬁnition of sine, cosine and mes and the law of cosines to be seen in '[k Chapter 9. (25 points)
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Y‘m‘S‘D" Yam («lClo “We: X = ' S\'V\(C_L: XVM9D°J w cyxk: ghmsootale" 251‘316“ (/Wuu)
kmS‘O" YMZ‘V «8v: 27,35‘16b V. If a wheel rotates with an angular velocity of 6.5 radians /sec. , how many revolutions of the wheel take place in 1 minute? If it is the wheel of a bicycle, and if the wheel has a
diameter of 29", what is the distance travelled in 1 minute? (10 points) lV‘QVMCmA Cev‘v‘covwaﬁ l‘o 2W QAMQMxLL $0 wake NC 609 X60 a: GZTCNI'MCA
ZTT deWMt ‘M‘W‘J‘Q—‘A P“ ’W‘C‘RWTG 2' (GMQQK GeroVaMo’n CV\ FNMW\X R
; (saw) x 2:3 = 5’, 655'”
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 Trigonometry

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