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Unformatted text preview: Math 113 EXAM III, April 19, 2004, (1 hour). NAME: SECTION: Instructor: WHENEVER POSSIBLE, GIVE EXACT VALUES. TO RECEIVE CREDIT FOR AN ANSWER,
YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. I. ‘ (35 points)
A boat is going straight north. An island is seen at an angle of 20" east of north. After
a mile, the same island is seen at an angle of 25° east of north. How far is the boat from
the island at the time of the ﬁrst sighting and at the time of the second sighting? How close to the island will the boat go, if it continues in a straight line? Neal‘aht'QiV , 6W QC 1 0) vsoi' kc heath
i 1 a» \ II. Evaluate the length L.
L a»! cl cm" was = If: 31+ 52 z (3 m coo 55" (10 points) Lzlf.‘
A III. 3 (6+29» points) 1) Find a solution to each of the following equations (keep EXACT values. You are NOT
asked to ﬁnd all solutions). (i)sin:v = 0083?”. C09 3T: 5&(I3§"”).So 3C2W 3W::’Ell~‘ Lo aOale/lo“ z 3‘? t (ii)sin6 = —cos3?". a: '1": m a OM'W bu‘Mq 9Q y; bu‘v‘ 1%—
O o 2) Find all solutions to the equation 1 sin26—cos202 5, in the interval [—27r , 0]. Z
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do: waL9:l_Cop'9)MA3¢K\ 2.01% M— IV. Determine the weight W and the angle a so that the ﬁgure shows an equilibrium
position. (35 points) oqugmec. AM‘W
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L h “ M‘W F3 ‘3 o bCMSSO
p!” (30m53, >/\ 0
E12<WAU3~°<)NC07°(> (may)? “1725
_7 __’ 0 55° 0
F3 2 4 o ) 3 > MA W: 3% A; LI
_. —w \\ ~> ‘ FM"
Fy‘TFLTr3ZO V. (25+10 points)
1) On a river ﬂowing south with a current of 3 mi/ h, a boat cruises at a speed of 4 mi/ h. The river is .4 mi wide. On the 355mm bank of the river there is a point A.
it is point A’ on the ﬁtern bank. What should be the compass heading of the boat in order to reach point A’
starting from point A. How much time will it then take to cross the river? TR“ {cogent macaw/3 (in «Mm/3M at (397*
V090qu VCJ‘M . bole.223; opvs 9:: 43.50 (WVM’AQ/‘faoliwa “mild6°: mt“)
tune  1.54 (MM) Directly across 395‘“ _ 2:. 45’ 9‘0qu p‘ue‘k 2' 61" g 0} inu‘vx tS 2) Now assume that a boat (on the same river) cruises at a speed of only 1 mi/ h. Starting
from point A7 can that boat reach point A’? Justify your answer. Explain how the ﬁgurAeK below is the key for answering the following question: what should
the heading of the boat be in order to land as close as possible to point A’? \l‘c’) CW 001% V0 Y‘caJlA A, \JJ'tCW dtxu: no
t’U‘mAVKQA [MAJA do 1 3 (“pair/W MM Le (or: em 0&ov3‘g “BM\A‘ﬁ‘bvdA‘OAVl/‘WN‘.~\_ \ '\\ J31 \7 \ “(gublmaAA WvJouN‘,\/~Q \ Oak/tarrka Mi, mm! aveMoeﬂmMQObi
~\\ \ktwotdw “tow”?ka mevam ...
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 Spring '07
 ROSAY
 Trigonometry, Following, Christopher Nolan, exact values, OM'W bu‘Mq 9Q

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