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Unformatted text preview: MATH 1613 Section 009 Printed Nam ' This exam is worth 100 points. You must show work to receive full credit. You may use
any statement from the book and the class as long as you clearly state what fact you are using. Good Luck! Show All Work (1) (8 points) Solve the trigonometirc equation for 0 g 9 < 360°. _ ﬂ 0056’: —
2 $3: . {‘ Q‘L 1,; a (2) (12 points) Solve the trigonometirc equation for all real 2: in radians. 2COSZ$ = ﬁcosx at (Q ‘ _WMWM:«m :. [r my» (3) (10 points) Solve the trigonometirc equation for all real 6 in degrees(to two decimal degrees). 2tan6—320 sin a sin 6 sin 7 a b C * The law of sine: * The law of cosine: 02 = a2 + b2 — 2ab cosd 4 12 points Solve the trian 1e given the indicated measures of sides and angles.
g
5 = 36° 7 : 43° a 2 10cm s ‘ e A
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r; v a ‘ . I 'v. {124K (5) (8 points) Find two possible angles for 3 of the two traiangles given the indicated
measures of sides and angles. a2350 az7ft b=9ft if A“;
g f, x 543 a ._ :13?“ f3 is“
. It: ‘
m '7‘“ ‘ n—‘x inh‘ j K‘ \ V“ 1},
. 2 a .
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I x L, a k ,7 _ \s A “ , ; \l w W" , . x _<‘ L» .m {J [ ~ ‘ji " ., 9" (6) (15 points) Two sides andthe included angle are given as theAfOilowing a = 65° 2 7mm x 11mm ca. 8: ‘1, "’ a F' i (a) (7 points) Find the side a. . * .
z“ 43 ‘ if ‘ *3”
«1"
I” . z,
"y" {if .1 7‘ ‘ W Y: i '3” » w (X , H 2 “M if s T M av ) U” a i‘ (b) (8 points) Find the area of the triangle by using Heron’s formula. 5(5 * a)(s — b)(s * 0)) i ﬁt: w"? ﬂ b
I'M“? 1“ e: 1 W25!"
ii [Ni (7) (10 points) Two boys pull a wagon, one with a force to 60 lbs, and one with a force
of 45 lbs. There is an angle of 35° between the two boys. (a) Draw a picture of the two force vectors, and the resulting force vector. /~»> “’7‘ (8) (5 points) Find the angle between the vectors u =< 1, 2 > and V :< 3, 2 >. AW? 0? 905/1099 (hint: 0089 = ’l 7,7? 3; . :7 hr (‘7 I f “ 1? W"
or X f, z! —)
[0) 46/ f5 2 meme
4 (9) (12 pts) For the vector u :< 074 >, v :< ~2,3 > and w :< 071 > perform the
indicated Operations. (a) u+v ,/ <4ng Av\v\\ _ 1’ ’ . g3 (4”; (10) (8 points) If u : 2'27 ~ 6j and V 2 3i + j7 com 1%efdlowm‘g.»
L l “(9 3 ( [2% 5 {V
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vs" 1 ...
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 Fall '08
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