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# 01faex3 - K I ’ MATH s13 Hut 2001 —RDSA‘1 90wa Math...

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Unformatted text preview: K I ’ MATH s13 Hut. 2001 —RDSA‘1 90wa Math 113 EXAM III, Nov. 29, 2001, (1 hour). NAME: SECTION: Instructor: To receive credit for an answer, you MUST show work justifying that answer. p WHENEVER POSSIBLE, GIVE EXACT VALUES. I. (30 points) A plane maintains a compass heading of 20" east of north, but due to a south Wind the plane is going in the direction of 17° east of north. If the ground Speed of the plane is 380 mi/h, what is the speed of the wind? ’ Ex»? II. (25 points) 1) Draw the graph of the function y = sin 2:1: . . M wmmmaa: 2) Find A and D such that the graph below is the graph of the function y = Asinx + D. 7’ - 3) Find C so that the same graph is the graph of the function y Acos(x + C) + D. . 4) If this is the graph of the cosine function, show clearly on the an axis the numbers 2:0 : cos*1(:§2.), and 9:0 -— 27r. Explain. III. (20 points) Show by a simple argument (e.g. what is the sign of the right hand side if :37: < :c < 0?) that one of the two following identities is wrong. Then, prove the other one. 2 cos 22: cos :1: = 1 — tan2 :1: . 2 sin 213 3111 x = i % g z ‘ § . 3 5 é % i l—tanzx' umm Mama." .V .., .. m .‘.~.MM,;.MN,L..M;- ,.w..«.-¢w;m.,g.w u... m . “hum”, .Ww ‘ . Wm. M i z ,E g a .5 3 a i 5, x Y 3 i 1 a x 'IV. (25 points) Let [7 = —35— 2;, with i and the standard basis vectors (if you prefer, you can use the notation < —3, —2 >). Let S = i+ 53' (use < 1,5 >, if you prefer). 1) Evaluate the length of the vectors [7 and S". _ "murakmmmm « ‘1 v 2) Compute the dot product [7 - S" 3) Give the EXACT value of the cosine of the angle between these 2 vectors. 4) Decompose g into the sum of a vector proportional to (7 and a vector perpendicular to g. ' WNW mm «mm» M. .u ..,.».,,l,uu.wm.m. .u‘ ‘Aunrvyhvtms v ,7 WW .m.mw;w.m4 w, hmmmmnumam .W i. . V. 1) Find to such that sinto : cos(g-) .and 0 S to g (20 points) 2) Find all solutions to sint = cos(%), in the interval [—7r , 2w]. (If you have not found the answer to 1, leave your answer in terms of to). 4 VI. This ﬁgure shows an equilibrium, the left cable is horizontal. The weight on the right (2M) is twice the weight (M) on the left, and the middle weight is W. Determine the angle oz. Is it possible to determine the weights M and W? (20 points) ...
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01faex3 - K I ’ MATH s13 Hut 2001 —RDSA‘1 90wa Math...

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