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Unformatted text preview: rmATHlIS swarm: 20m —Ros~1 4 . FWM __ ’7 Math 113 FINAL EXAM, May 18, 2001, (2 hours).
5 NAME:
SECTION: Instructor: I. On this ﬁgure, lOC’l = 4, and [OB I = 2, and the are AB is an arc of the circle of radius
2, with center at 0. Give the exact value of the angle 6 shown on the ﬁgure, in radians and in degrees.
Evaluate, EXACTLY, the perimeter and the area of the shaded region. C radians = 0 . l area of shaded region 2 \ t perimeter = 1 Mug/unwananamnuwanwww mmj m4 mammmm HymnMina”wwwmmpm mm“ II. Give EXACT values. cos(;8:) = sin(—‘8—”) III. Evaluate EXACTLY sin (tan'1(—2) + IV Let y($) = Asin(B:c + C) + D, with A > 0. If‘the maximum value of y(:z:) is 5,
and the minimum value is 4. What can youysay about the constants A , B , C, D ? If, additionally, you know that y(0) = 4.5, what else can you say? This is the graph of the cosine function. Evaluate the abscissae x1, $2, $3, 334, x5, x5, x7
and $8 shown on the ﬁgure. The answer is to be given in terms of 0 (0 shown on the ﬁgure)
Which .73] is equal to cos—1(cos 6)? Justify your answer. if“ f E
i V. If there is aIWind of 55 mi/h, blowing from the SOuth, which compass heading
should a plane, ﬂying at 500 mi/h (speed relative to air), keep in order to go in the
direction of 200 west of north? WMWMWVMMquuxrwwfﬁ, ﬂy mmno a“, ‘ Wm WM , ,v t u m wwwmmwwn, «:mummmvmmﬁwr'“InmeMnMA‘Ly mum.” D0 only one Of the two problems VI A a
for both. VI A.
Determine the angle
a, so that this
is an equilibrium
assume no friction). VI B. You cannot get credit VI B. Let X = 4?. 75' an . d 2 2 25+ Evaluate the lengths of these vectors and
their dot product. ' ~ Give the EXACT Value of the cosine of the angle between these two vectors. Is the angle
aCUte 01‘ Obtuse (d0 not use your calculator)? Write 17.116 VeCtordX as the sum of a vector parallel (proportional) to Z, and a vector
Perpendlclﬂar to 2 D0 not apply a memorized formula, justify your result. Answer t0 VI A7 Or to  n _ — _ _ _ _ _ _ ' ‘ ‘ ‘ ' ' r    —  — — _ _ VII. 1) Let z be the complex number 2 = 1 — 2‘. Write z in polar form (rem). Evaluate
28 and %, both in polar form, and in rectangular form. 2) Evaluate the square roots of (1 — i), in polar form and in rectangular form (you
may use the result of problem II). ...
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 Spring '07
 ROSAY
 Trigonometry, Complex number, Euler's formula, shaded region, exact value, polar form

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