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00fafin - "4mm PM 200° ‘ 905*“ Manama” A A...

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Unformatted text preview: "4mm; PM» 200° ‘ 905*“! Manama” A , . . A. Wfiammwwmmm Q FINAL EXAM, December 18, 2000, ( 2 hours). To receive credit for an answer, you MUST Show work justifying that answer. WHENEVER POSSIBLE, GIVE EXACT VALUES. 1. The figure shows a circle of radius 2, with center at 0. (30 points) 1) What is the exact measure of the angle LAOB, in degrees, and in radians? 2) Evaluate the area, and the perimeter of the shaded region. 3) Determine the exact values of the sine, cosine and tangent of the angle 6 shown on the figure. {rm ‘1 F L . K 03 II. The total of the two masses M1 and M2 is 101b. Find M1 and M2 so that this is an equilibrium position? (30 points) III. (30 points) On a river flowing directly south-west (i.e. at a compass heading of 225°), at a speed of 2 mi/h, a boat maintains a compass heading of 67.50 (i.e. towards east—north-east). At which speed (relative to the water) should the boat travel in order to cross the river, going straight east? myw“.......mmw. V. is i .t , /’””~ I ‘y‘ A.V.-A_ .V, M .H.‘ . . H A IV. (30 points) Find all solutions to the equation 2 cos2 a: - (1 + tam2 tr) = 2, in the interval [0 , 2%]. V. (continued on next page) (25 points) 1) Draw the axes, and indicate very clearly some points on both axes, so that this is the graph of 1 + sin 2x. E E 7% 2) This is the graph of cos 1:. With a and 6 as shown on the figure, is 6 = cos—1(a)? l (25 points) f. Evaluate l, and l (the lengths of X and T), and e of the angle between these btuse (do not use your calculator)? VI Let X =3z' + 4j,‘ andT = 2;? — 3] the dot product X - T. Give the EXACT value of the cosin two vectors. Is the angle acute or 0 vector proportional to T and a vector A7 perpendicular Decompose X into the sum of a to T. «mm «1mm,» WWW. m” VII. Let 2 be the complex number: (30 points) z=\/\/§—1—i\/\/§+1. Evaluate z2 in rectangular form (x + iy). Then, write 2:2 in polar form (re . mammnmmvw‘m‘nmww l; l is). What are the tWo square roots of 22, in rectangular and in polar form? Write the complex number 2 in polar form. Write the complex number i in polar form and in rectangular form. M.._w.u.m..t.m.m M/ u, ,. ...
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