In Problems 57–60, write the equation of a sine function that has the given characteristics.57. Amplitude: 3Period: π 58. Amplitude: 2Period: 4π 59. Amplitude: 3Period: 2 60. Amplitude: 4Period: 1

1. The average monthly temperature, y, in degrees Fahrenheit, for Alaska, can be modeled by 2n y = 16 sin (x -#) + 40, where x is the month of the year (January = 1, February = 2, ..). Find the amplitude and explain what it means in relation to this problem. (4 points) b. Find the period and explain what it means in relation to this problem. (4 points) C. Graph the function for 1 S x < 12. (4 points) d. What is the highest average monthly temperature? In which month does this occur? (4 points) a. 2. Sketch a reasonable graph that models the motion of a diving board vibrating 13 inches in each direction per second just after someone has dived off. (4 points)

Question 3 i. Find the real root of the given function f(x) = e²x -x-6=0 by Newton-Raphson iterative method and corrected to three decimal places. ii. Find the root of 3x+sinx-e* = 0 by Regula Falsi and Secant method correct upto two decimal places, use the initial approximations as 1 and 2.

18. A Ferris wheel is standing 4 feet up from the concrete floor of a park. Its diameter is measured as 26 feet and the wheel rotates once every 32 seconds. If you start the ride sitting in a chair that is 6 feet above the ground, how high will you be 10 seconds after the wheel starts moving? During the first minute, when will you be 20 feet high? (Hint: start by modelling the wheel's movement as a trigonometric function.)

Problem 5. Use an addition formula to show that v2 cos x- |= cos x+sin x. Graph one period of the function f (x)=cosx + sin x.

Example 3 4/3 30° y

5. A 14 TT/2 3/4 5TM 3TT/2 -3 -2 -1 -1- -2- -3- -5- 2π 9414 Use a sine function. Vertical Shift Amplitude Period Horizontal Shift EQUATION: