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Unformatted text preview: Math 113 FINAL EXAM, Dec. 20th, 2007, (2 hours). NAME: ' SECTION: Instructor: lNO CALCULATOR means: NO CALCULATOR.I I. NO CALCULATOR. (20 points)
Give the EXACT value of BD (the length of the line segment from B to D). B II. (With calculator). Assume that the triangle OAB has an area of 3 sqft, and IOAI = 4
ft. Evaluate the angle 6 in degrees AND in radians. Evaluate the length of the arc of circle
from C’ to A, and the area of the shaded region (in terms of 0 if you were not able to ﬁnd 6). R V (30 points) ANSWERS: 6 = radians 0 Length of arc 2
Area of shaded region : III. No CALCULATOR. ‘ .  ' (25 points)
Find all solutions to 1 + tan2 6 = 16 sin2 6, with ~19? g 6 g ' IV. A hiker walks 3 miles in direction of north, then 3 miles east and ﬁnally 1 mile in
direction of 30° south of east (i.e. a heading of 120°). What is the distance (’as the crOw
ﬂies’) from the starting point to the end point? (25 points) r V.
Graph 3/ = 2cos 2 7' \I
x — —..
( + 2) 1 3 (30 points) \/ { VI. (20 points) 1). What are all the complex cube roots of —8? 2) Find a complex number 2 such that (1 +2i)z = (1 +32) (2 in Cartesian form a + bi). MM
VII. (25 points) 1) Given sing = % and 32'— S 6 S 7r. Evaluate cos 6. Evaluate c053 and sin 3. (NO CALCULATOR) 2) Find a square root of the complex number z = —2\/§ + i. VIII. A river, ﬂowing south, is .1 mile wide. The speed of the current is 4 mi/h. A
swimmer leaves the west bank at point A. Point A’ is straight across the river on the other
bank. The swimmer swims at a speed of 1 mi/h. If the swimmer swims with a heading
of 400 east of north, how far south of A’ will the swimmer land, and how much time will
crossing the river take? ’ I _ (25 points) For 10 points of extra credit ( explanations required): What should the heading be for the
swimmer in order to land as close as possible to point A’, and then, how far south of A’
will the swimmer land .9 What should the heading be in order to have the shortest crossing
I time, and what would then be the landing point? ...
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 Spring '07
 ROSAY
 Trigonometry, Complex number, Mile, shaded region, swimmer swims

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