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11B Topic 4_2

11B Topic 4_2. 6. Applications of periodic functions. Challenge Question (1). High tide is 4.5 m at midnight Low tide is 0.5m at 6am Find the height of the tide at 7pm? Between what times will the tide be greater than or equal to 3m?.

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11B Topic 4_2

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  1. 11B Topic 4_2

  2. 6. Applications of periodic functions

  3. Challenge Question (1) High tide is 4.5 m at midnight Low tide is 0.5m at 6am • Find the height of the tide at 7pm? • Between what times will the tide be greater than or equal to 3m?

  4. High tide is 4.5 m at midnight Low tide is 0.5m at 6am • Find the height of the tide at 7pm? • Between what times will the tide be greater than or equal to 3m? iii) Find “B” Period = 12 • Use y = A cos B(x+C) + D • Find “A” • Tide range = 4.5 - 0.5 = 4 • A = 2 • y = 2cos B(x+C) + D ii) Find “D” D = 4.5 – 2 = 2.5  y = 2cos B(x+C) + 2.5 iv) Find “C” We can see from the graph that no C-value is needed

  5. By use of TI calculator… • What is the tide height at 7pm? • Graph using suitable windows • 2nd Calc  option 1. Value • Enter 19 • Answer = 0.77m (2D.P.) • Tide above 3m • Add y = 3 to the graph • 2nd Calc  option 5. Intersect • Follow prompts • Answer = • MN – 2:31am • 9:29am – 2:31pm • 9:29pm – MN

  6. Challenge Question (2) High tide of 4.2m occurs in a harbor at 4am Tuesday and the following low tide of 0.8m occurs 6¼ hours later. If a ship entering the harbor needs a minimum depth of water of 3m, what times on Tuesday can this vessel enter?

  7. Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time: (a)Find the period and amplitude of the movement. (b) Predict the displacement at 10 seconds. (c) Find all the times up to 20 sec when the displacement will be 5 cm to the right (shown as positive on the graph)

  8. Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time: (a) Find the period and amplitude of the movement. (b) Predict the displacement at 10 seconds. (c) Find all the times up to 20 sec when the displacement will be 5 cm to the right (shown as positive on the graph) Period = 4.5 - 0.5 = 4 sec

  9. Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time: (a) Find the period and amplitude of the movement. (b) Predict the displacement at 10 seconds. (c) Find all the times up to 20 sec when the displacement will be 5 cm to the right (shown as positive on the graph) Amplitude = 8

  10. Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time: (a) Find the period and amplitude of the movement. (b) Predict the displacement at 10 seconds. (c) Find all the times up to 20 sec when the displacement will be 5 cm to the right (shown as positive on the graph) Since the period = 4 sec Displacement after 10 sec will be the same as displacement after 2 sec = 5.7cm to the left

  11. Model: The graph below shows the horizontal displacement of a pendulum from its rest position over time: (a) Find the period and amplitude of the movement. (b) Predict the displacement at 10 seconds. (c) Find all the times up to 20 sec when the displacement will be 5 cm to the right(shown as positive on the graph) Displacement= 5cm  t = 1.1 5.1, 9.1, 13.1, 17.1 3.9 7.9, 11.9, 15.9, 19.9

  12. Exercise NewQ P 179 Set 5.2 1,3

  13. Model: Find the equation of the curve below. y = a sin b(x+c) Amplitude = 2.5

  14. Model: Find the equation of the curve below. y = 2.5 sin b(x+c) Amplitude = 2.5 Period = 6  6 = 2/b b = /3 Period = 2/b

  15. Model: Find the equation of the curve below. y = 2.5 sin /3(x+c) Amplitude = 2.5 Phase shift = 4 () so c = -4 Period = 6  6 = 2/b b = /3 Period = 2/b

  16. Model: Find the equation of the curve below. y = 2.5 sin /3(x-4) Amplitude = 2.5 Phase shift = 4 () so c = -4 Period = 6  6 = 2/b b = /3 Period = 2/b

  17. Exercise NewQ P 183 Set 5.3 1,4

  18. Exercise 5.3 pg 183, No.4

  19. Find the equation of the curve below in terms of the sin function and the cosine function.

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