XXXXXXXXXX I need this completed at a high school advanced functions university prep level. All answers must be displayed with a full solution to how it was solved.

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I need this completed at a high school advanced functions university prep level. All answers must be displayed with a full solution to how it was solved.


MHF 4U - Dusome Week #3 Assignment – Trigonometric Functions Neatly answer all questions in the space provided. You must show all work to receive full marks. Partial marks will be awarded. Good luck! 1. Complete the chart below by stating the amplitude, phase shift, period, and vertical displacement of each trigonometric function. Be sure to indicate the direction (left, right, up, or down) of the vertical displacement and the phase shift. [16] Function Amplitude Phase Shift Period Vertical Displacement ? = −2???6? ? = 4 5 ??? [ 2? 7 (? − 6)] ? = 5 + cos 1 2 (? + ? 4 ) ? = −4 cos (3? − ? 2 ) + 2 2. Sketch the graph of each trigonometric function for ? ∈ [0 ,2?]. [6] a) ? = ???? b) ? = ???? 3. Fill-in-the-Blanks: Provide answers to the following questions in the space provided. [6] a) State the maximum value for ? = 3???3 (? + ? 3 ) − 7 ___________________ b) The minimum of a sinusoidal function is -4 and the max is 8. State the amplitude. ____________________ c) State the domain and range of ? = −4???3 (? + ? 6 ) − 2 ____________________ ____________________ d) The zeros of ? = ???? are ____________________ e) The Maximum of ? = sin ? is ____________________ 4. Determine an equation for the sinusoidal function shown. [3] 5. Sketch the graph of ? = 3 sin (? − ? 6 ) − 1 over at least one cycle [5] 6. Sketch the graph of ? = −???2 (? + ? 3 ) + 3 over at least one cycle. [6] 7. John is riding the Ferris wheel at the county fair. The minimum height of the seat is 1.3 m and the maximum is 49.3 m. The ride takes 90 seconds to complete one full revolution. [13] a) Sketch the graph that represents this situation (2) b) Write an equation for the function. (3) c) What is the radius of the Ferris wheel? ________________________(1) d) When does the maximum height occur? ___________________(1) e) Use your equation to find the height of the rider when t=20 seconds (2) f) For what interval of time is the height of the rider 30 metres or higher (one revolution only)? (4)