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01fafin - “Aw.mw—MM‘W_W “M mpg—u n3 Mm 200 ~...

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Unformatted text preview: “Aw.mw—MM‘W..__W., “M--- mpg—u n3 Mm. 200! ~ EDSA‘t “v...‘_.w.....,...~wm< “I We . i , .. wummw Math 113 FINAL EXAM, Dec. 21, 2001, (2 hour). NAME: SECTION: Instructor: To receive credit for an answer, you MUST show work justifying that answer. WHENEVER POSSIBLE, GIVE EXACT VALUES. I. Note that the circle shown on the figure is a circle of radius 2 (units), not of radius 1. Determine the osine, sine and tangent of the angle 6 shown on the figure. (15 points) (20 points) Does a: = tan—1(—3)? (Yes, possibly, or no. Justify your answer.) i E '1 i III. If a sector of a circle of radius 6 has an area of 47r (units), what is the exact measure of the angle at the center, in radians and in degrees, and what is the length of the corre- sponding arc of circle? (16 points) wme , M t , IV. Let (7 and l7 he the vectors shown on the figure. Evaluate the dot product (7 - l7 . Is the angle 9 aCUte 01' Obtuse? Do not useyour calculator. (14 130th5) “A .4»— MWMMMu—thpun V. > (30 points) 1) Determine A, B, D so that the following graph is the graph of the function A cos(Bx) + D, with A and B > 0. 2) What is the abscissa a: of the point M shown on the figure, and what is the ordinate y of the point P? 3) With A, B, D as above, determine C, so that the same graph is the graph of Asin(Bx + C) + D. (If you did not answer the first part of this problem, you can give here your answer in terms of B.). ‘ W‘m . ‘I [A . V. N u méwmwnm. . “mi-7k ‘mummzrzymummmwm WWWMM... M . “l VI. Let 2 be the complex number 2 = —2 +221 (30 points) 1) Write z in polar form re”. 2) Evaluate %, in polar form and in rectangular form. You are asked to do the two computations independently (e. g. for getting % in rectangular form, do not make use of your calculations in polar form). 3) Evaluate z2 in polar form and in rectangular form (Same, do two independent computations). 4) 2 has three (complex) cube roots. One of them has both its real part and its imaginary part positive. Find it, write it in rectangular form. w....w.m. a «11.: 1., W. m Cm numaui/«kuipdmvmmhxflméflw mam-inmate \ numim: mth am: ,‘mhmmn .. “tannin”. . ...,t.i.imi..w...,; M H w VII. A plane flies at a ground speed of 550 mi/h. The speed of the plane with respect to the air is 560 mi/h. The speed of the wind is 30 mi/h. What is the angle between the direction towards which the plane is heading and the actual direction towards which the plane is going? (30 points) VIII. Find the angle a in order that this is an equilibrium (assume no friction). You MUST explain your solution. (15 points) lleo (30 points) sin(a;+-g) — sinx = .0 , —27r§x§27r. f % g E S i g ...
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