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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
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'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. . “mi7k ‘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 maminmate \ 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
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 Spring '07
 ROSAY
 Trigonometry, Complex number, Euler's formula, polar form

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