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MATH 43,3 Rog/AX  plum, Â« swam/(7 2007, â€œ8 Math 113 4 Spring 2002 â€” Final Exam Name:___________________ Signature: Instructor: (a) To receive credit for an answer, you must justify that answer. No work no credit. (b) Whenever possible, give EXACT values. 1. Find the length of the line segment AB. Keep exad L/alMLâ€™ï¬. ' ( 15 pts) 2. Find the area of the shaded region. Keep exacf" Vaflgles, ( 15 pts) g. Let @1
ll ï¬‚=2i~3j, â€™i+2j.
(a) Find the dot product 1?  27. ( 5 pts) (1)) Find vectors (â€™1â€™, 5 such that 77 = (â€˜1â€™ + 5, ('1' = MI, and his orthogonal to 17. (15 pts) (0) Find the angle between {I and 17 (you may use calculator). (5 pts) .4,~'~4< wï¬wm ,,. , .um mmÂ» m m, â€œMMâ€œ... . The following is the graph of y = ASin(B3: + C) + D. E} (a) Find A,B,C, D with A > 0 and B > 0. (b) The above is also the graph of y = Aâ€™ cos(Bâ€™2: + C") + Dâ€™. Find C". (16 pts) (4 ptS) (Warning: No credit will be received if calculator is used.) , Find the following exact values: (a) cosâ€”1(cos(%)) (5 pts) 1 .
 â€”1
(b) sm(cos (â€”4) â€” 7r) (10 pts) 5 â€˜3 3â€˜ . . 2 g (c) smx, for x w1th cosa: = 5 and 77r S :c g 87r. (10 pts)
5 . 5 '5 g 5 5 Â§ 5' 5 (d) tan :5, for the same :1: in (c) (5 pts)
5 5 g f E A boat .
E . is to travel to a destination that is 400 east of north from its departure pomt. 0 will encounter a current ï¬‚owing due east at 10 knots.
0 will travel through the water at 18 knots. (a) With care, sketch a ï¬gure showing all given quantities. (5 pts) (b) (9 pts) Find the correct heading for the boat. State your answer in terms of degrees east of north. 3' (6 W) l 3 i i l :i Â§~ i i l (C) Find the speed of the boat relative to the river bottom.
i 5i E
i i ' . Z .
; (a) Given 2 = 2 â€”â€”z' and w = 1 + 41â€˜, write 2w and ii}â€” in the rectangular form. (8 pts) (b) Write z = 2 â€” 22' in the polar form. (8 pts) (c) Find all cubic roots Of 2 ~ 22â€™, and write each root individually (you donâ€™t need to give the
(8 ptS) rectangular form). k
l
g:
i3
3 (d) For the cubic roots in (c), write one of them in the rectangular form. (6 pts) .1 The following two objects are in static equilibrium. Assuming there is no friction, ï¬nd the angle
a, (Give the answer accurate to the 10th decimal place.) (20 pts) ,_ 9. (a) (15 pts) Write cosx â€”â€” sins: in the form Asin(Bm + C). (b) (10 pts) Find the exact values of all solutions to equation cosx â€” sinx : â€”\/Â§. ...
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 Spring '07
 ROSAY
 Trigonometry

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