Page 2 of 7 Vista Virtual School A3 2. Complete the table by determining the following characteristics of each function. (8 marks) Equation Amplitude Period Horizontal Equation Translation of Midline y : sin(x 3) +1 )1 : 6 sin 0.25(x + 45) 9 y 2sin8(x+3)+5 - y : 0.75 sin 4(x * 60) 3. The graphs of two sine functions, y = a sin(bx + c) + d , are shown below. Compare the values of the parameters a, b, c, and d for both graphs. Which would be the same and which would be different? Explain your answers. (4 marks) Graph 1 300 50 Y 6 O Page 4 of 7 Vista Virtual School A3 5. Determine if each set of data is best represented by a linear, quadratic, exponential, or sinusoidal regression equation. Where possible, state the coefficient of determination r2, for each equation. (6 marks) Table\" x -3 -2 _1 0 1 2 3 y 0 -4.5 -4.5 0 4.5 4.5 0 Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yesfno): Best type of equation: Table 2: x -3 2 -1 0 1 2 y -6 -4 -2 0 2 4 6 La.) Linear equation coefficient of determination: Quadratic equation coefcient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yeso): Best type of equation: Table 32 x _3 _2 _] 0 1 2 y 9 4 1 0 1 4 9 DJ Linear equation coefficient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yesfno): Best type of equation: Table 4: x -3 -2 -l 0 1 y 0.125 0.25 0.5 l 2 4 8 IN.) LA Linear equation coefcient of determination: Quadratic equation coefficient of determination: Exponential equation coefficient of determination: Sinusoidal equation (yesx'no): Best type of equation: Page 5 of 7 \\NS: 302 A8 21/22 Sem 6. The Niagara SkyWheel is a Ferris wheel in W Niagara Falls, Ontario. Instead of seats, visitors so ride in capsules which they enter and exit at the lowest point of the ride. The graph to the right models the height of a particular capsule over the course of a ride. 50 40 30 height (In) 20 10 {I 12 24 time (min) a. State the value of each characteristic of the graph above and explain what it represents in the context of the question. i) amplitude (2 marks) ii) period (2 marks) iii) y-intercept (2 marks) iv) midline (2 marks) v) range (2 marks) b. Determine the equation of a function in the form h = asin(bt l.57)+d , where it represents the height, in metres, of a rider above the ground, and t represents the time, in minutes, after the ride has started. Express the values of a, b, and d to the nearest hundredth, if necessary. (2 marks) Page 6 of 7 Vista Virtual School A3 7. Each evening at sunset, the lights on the Niagara SkyWheel are turned on. The time of the sunset in Niagara can be modelled by the equation 5 =2.89131n(0.016d l.183)+18.512 where s is the time of the sunset, and d is the day of the year. a. Use the equation to determine the time of day that the sun sets on July lst, which is day 182. (2 marks) b. On how many days of the year, to the nearest whole number, will the lights be turned on at 8 pm (20:00) or later? (2 marks) \f