Pre-Calculus: Chapter 4 Review Name: ______________________ This are problems that supplement the textbook review: pg.439: 1,5,13,19, 23, 29, 33, 35, 37, 41, 5155, 63. 75, 79, 81, -- 71, 85, 87, 97, 102 1. Find the exact values of the six trig functions of the angle Ѳ shown to the right. 2. Find the five remaining trig functions of Ѳ, given 6 that sec , tan 1 5 3. On graph paper, graph the function for two full cycles: y 2 cos( x) 3 1 x y sin 2 4 4. Find an equation for the following graph. 5. Kylie measures the angle of elevation from a point on level ground to the top of a building 120 meters high to be 32o . She walks towards the building until the angle of elevation is 45o . How far does she walk? 6. Find all values of theta between 0 2 that satisfies the following equation. Do not use your calculator for part a. a. cot 3 b. sec 1.743 7. The following graph shows the depth of water, y metres, at a point P, during one day. The time t is given in hours, from midnight to noon. (a) Use the graph to write down an estimate of the value of t when (i) the depth of water is minimum; (ii) the depth of water is maximum; (2) (b) The depth of water can be modelled by the function y = A cos (B (t – 1)) + C. (i) Show that A = 8. (ii) Write down the value of C. (iii) Find the value of B. (6) (c) A sailor knows that he cannot sail past P when the depth of the water is less than 12 m. Calculate the values of t between which he cannot sail past P. (2) 8. A Ferris wheel with centre O and a radius of 15 metres is represented in the diagram below. Initially seat A is at ˆB = π . ground level. The next seat is B, where AO 6 (a) Find the length of the arc AB. (b) Find the area of the sector AOB. (c) The wheel turns clockwise through an angle of 2π . Find the height of A above the ground. 3 The height, h metres, of seat C above the ground after t minutes, can be modelled by the function π h (t) = 15 − 15 cos 2t . 4 (d) π . 4 (i) Find the height of seat C when t = (ii) Find the initial height of seat C. (iii) Find the time at which seat C first reaches its highest point.
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