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Unformatted text preview: MATH 44?» *Rosrw EXAMﬁvg swam/(r 2mg Name: Instructor: Math 113 — Spring 2002 — Exam 111 Signature: 1265 ‘17 (a) To receive credit for an answer, you must justify that answer. N 0 work no credit.
(b) Whenever possible, give EXACT values. Problem
1 5 Total Points
25 2 25 3 20
4 25 25 6 20 140 Scores 1. A boat
0 is to travel to a destination that is 30° west of north from its departure point (on the south
bank of an easterly ﬂowing river).
0 will encounter a current blowing due east at8 knots.
0 will travel through the water at 12 knots. (a) With care, sketch a vector diagram showing all the given quantities. (10 pts) (b) Find the correct heading for the boat. State your answer in terms of degrees east or west of
north (to the nearest degree). (8 pts) (c) Find the speed of the boat relative to the river bottom. (7 pts) 2. The weight and pulley system indicated below is in static equilibrium. (a) Express the force acting along each line in terms of the unit vectors land . ( 10 pts)
0 Along line@
0 Along line®
. Along 11ne® (b) Find the weight w (accurate to the tenth decimal place) and the angle 6 (to the nearest tenth
degree). (Hint: you may need identity M sin(Bt) + Ncos(Bt) : M2 + N2 sin(Bt + C),
where C is any angle with (M , N ) on its terminal side.) (15 pts) 3. Let tanx = 1—52 with —7r < :r < O.
(a) Find the exact values of sin(2:1:), 008(2z) and tan(2x). (10 pts) (b) Find the exact values of sin ;, cps; and tan E. ' (10 pts) 4. (a) Draw the graph of 1 , y : ——2—sin(2x— for— 27r g x g 277.
Label the :c—intersepts and the coordinates of the points at which the y—value is the largest
or the smallest. VJN (18 pts) (b) Determine the values ofA, B, and C (with B > 0 and —7r < C 3 7r) so that y = A cos(B2:+C)
has the same graph as that of the function in (a). (7 pts) 5. The graphs of y = 3 + 251nm and y : 4 are indicated below. Of interest are the points of
intersection. Determine the exact values of _
(a)(10 pts) x1 = (b)
(C) (5 pts) $3 = (d) 6. Determine which of the following are identities and which are not identities. If the equation is an identity, prove it. If it is not an identity, ﬁnd all values of x which solve the equation. (a) (2 sina: —— 1)2 = 1 (10 pts) (b) 2(0052: + l)(cosa: — l) = cos(2:r) — 1 (10 pts) ...
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 Spring '07
 ROSAY
 Trigonometry

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