I need help with my math homework

Assignment 5A: Trigonometric Functions Total: 35 marks Show your work for full marks. Reminder: You're welcome to use Desmos to verify your answers. 1. The graph of a cosine function is shown. [4 marks] a) What is the amplitude? _ , , v v v ' b) What Is the vertlcal translatlon? c) What is the period? 2. Consider the function f(x) = sin (3 (x + 9) 5. [4 marks] a) What is the amplitude? b) What is the period? c) What is the phase shift? A sine function has a maximum value of 8 and a minimum value of 1. [2 marks] a) Determine the amplitude of the function. h) Determine the vertical translation. Two consecutive peaks (maximums) of a cosine function are at x = E and x =3 [4 marks] a) Determine the period of the function. b) Determine the phase shift of the function. 6. The average monthly temperature in Toronto is 8.6C. The temperature fluctuates 13.1C above and below the average temperature. The coldest month is January (month = 1) and the hottest month is July (month = 7). [6 marks] a) Find the equation of a cosine function that models the temperature at a given month, T(m) . b) Use your model to predict the average temperature for March. Determine an equation that models the graph shown. [5 marks] A road is built up the slope of a hill with a height of h metres and an angle of elevation ofx. The length of the road (diagonally) is d. [3 marks] a) Sketch a diagram ofthis situation. Label all quantities. b) Find an equation for d that uses one ofthe reciprocal trig ratios. Use Desmos to determine all values of 0 S x S 211' for cscx = 7. You do not need to include the graph. [2 marks] The water depth in a harbour is 17.8 m at high tide and 10.2 m at low tide. One cycle takes 12.4 hours to complete. Determine a function, d(t), that models the depth d (in meters) of the water at time t (in hours) with t = 0 corresponding to low tide. [5 marks]