00spex3 - "Wm us sfizmo zoos g a «as, Name To...

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Unformatted text preview: "Wm us sfizmo zoos . . g/ a} «as,» Name; To receive credit for an answer, you MUST show work justifying that answer. WHENEVER POSSIBLE, GIVE EXACT VALUES. I. (25 points) 2 1) Find all solutions to the equation sin 30 = i, in the interval [2n , 47r]. 2) Solve the equation 3 t Lflzly @0934”, 1 — x/gtanzc Full credit will be given only if you find an EXACT solution (without calculator). Rewrite the right hand side as the tangent of some angle. II. On a river flowing south, at a speed- of 2 mi/h, a boat maintains a compass heading Of 450 (Le. towards north—east). At Whmh speed (relative to the water) should the boat travel in order to cross the river, going straight east? (20 points) III. Determine the angle a and the weight W so that the following be an equilibrium: (25 points) IV. _ (25 points) 1) If this is the graph of either Asin(Bx + C) + D, or Asin(Bx + C) + D, what is the period? 2) Determine A, B, D, with A > 0, such that the following graph be the graph of the function A sin(Bx) + D. 3) Determine A, B, C, D, with A > 0, such that the same graph be the graph of the function Acos(B:1: + C) + D. 4) Draw the graph of the function cos2(3:1:) (you can use the half angle formula, to figure out the answer). {W i V. Give exact answers: ‘ (10 points) sin(%fl) = sin—1(——‘é—§) 2 VI. Evaluate, exactly: (25 points) Sin(: + tan‘1 4). fig VII. Evaluate the length of the line segment AD. Give an EXACT answer. (20 points) i ( )Bd : 3 ) WWMMIWW ...
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