03fafin - Math 113, FINAL EXAM, DecemberIIS, 2003. (2...

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Unformatted text preview: Math 113, FINAL EXAM, DecemberIIS, 2003. (2 hours) SECTION: Instructor: II. For the angle 6 shown on the figure: points) 1) Give the exact values of Sr c036 = 5m6 : tan6 = 2) Give the exact value of COS(6 — 3) Give the exact value of 008(26 — III. Given that the circle has a radius of length 5 (units). Evaluate: The length of the arc of circle form A to B, the area of the triangle OBC' and the area of the shaded region. (25 points) ‘ IV. (25 points) 1) Draw the graph of y : 2sin(3:c + — 3. 2) If the graph below is the graph of y = Acos(Ba:+C)+D, with A and B > 0. Among the quantities A, B, C, D, which ones can be determined from the partial information that is given? Evaluate them. (25 points) Determine the angle 0 and the mass W so thatthe following is an equilibrium. VI. (This problem must be done without calculator. But you may of course ‘secretely’ use your calculator to see whether you missed some easy simplification.) (20 points) Find the exact value of the cosine of the angle 6 between the two vectors: (7’ =<4,x/§> , l7=<3\/§,7>. What is 6 in radians and in degrees? VII. Complex numbers. (25 points) 1) Let 21 =——1—z'andzg=1—z'. Evaluate 21 + 22, 2122 and i (in rectangular form a + bi). 2) Show the graphical representation of the complex number 21 = —1 ~ 2', and write 21 in trigonometric form ( r(cos 9 + isin 3) Find a square root (that you may denote by s) of (—1 —— in trigonometric form. Then, use the half angle formulas for writing that square root in rectangular form. 4) What are all the square roots of (—1 — i), in rectangular form? VIII. (25 points) 1) Find an angle 51:0 such that sin(m0) = — sin($) 2) Solve sin(w0) : —sin(§), for 0 g a: S 47r. 3) Solve sin2(xo) = Sin2(%)7 for 0 g :1: S 47r. IX. If cos 6 = % and 1275 S 0 g 0, which one of the following angles is equal to cos“1(%1—): 0, —6,7r——0,7r+6? A short but complete justification must be given. (5 points) ...
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03fafin - Math 113, FINAL EXAM, DecemberIIS, 2003. (2...

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