2. Write the equation of the function in the form of y = a sin b(x c) + d . a > D, and in the form 3; = amsb(xc)+d.a> 'I-nr 2 511:? As a sine function: As a cosine function: 2. A small plane is flying at a constant altitude of 3000 m directlvlr toward an observer. Assume the ground is flat in the region close to the observer [see page Zofor a similar example]. a] Sketch the graph of the function that represents the relation between the horizontal distance, in metres, from the observer to the plane and the angle, in radians, formed by the vertical and the llne of sight to the plane up to the point where the plane is directly overhead the observer. Be sure to include values a ong the horizontal and vertical axes. Your graph should include on v the portion of the function that corresponds to the problem. b} What is the equation of the vertical asymptote line? c} What is the domain of the graph}| d} What is the range ofthe graph}| 3. In some Caribbean countries, electric current makes 50 complete cycles each second and the voltage is modelled by V =1705in(1002rt). Use technology to graph the function. a) Sketch the function's graph over two cycles. Be sure to include values alon both axes and their units. b) What is the period of the current in these countries? c) Haw many times does the voltage reach 110 V in the first second? at. A Ferris wheel of diameter 20 m rotates such that it completes one revolution in 40 seconds. Passengers board the lowest car ata height of 3 m above the ground, and then the ride begins. a} Draw a graph representing the ridefs height above the ground over one complete rotation of the Ferris wheel on the grid below. h} Determine a cosine function with a phase {horizontal} shift of zero that models the height, h, in metres, of the car relative to the ground as a function of time, t, in seconds. c} Use the function you determined in part [b] to calculate the first time the car is 20 m above the ground. 4. Use a sum or difference identity to determine the exact value of each of the following. Express your answers in simplified radical form. {Even though your textbook does not, we aiways rationalize the denominator if there are radicaisi} llrr a. (3)516?J b. Ian 12 2. Solve to express the general solution to 5 sec 9 2 = 3 cos 9 using exact radian measure