1. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Learning Goals I can substitute and solve for values using a sinusoidal equation. I can analyze and interpret graphs of modeled periodic behavior. 38

2. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions A nail is stuck in a tire. The graph below and the equation represent the height of the nail vs how much the tire has rotated.

3. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions a) What is the diameter of the tire?

4. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions b) How high off the ground is the tire’s axle?

5. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions c) At what angle will the height of the nail be 9.7 cm?

6. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Pg. 328 #3 The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled by the sinusoidal function : h(t) = 5 sin[30(t - 5)] + 7 a) Find the maximum and the minimum values for the depth, h, of the water.

7. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Pg. 328 #3 The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled by the sinusoidal function : h(t) = 5 sin[30(t - 5)] + 7 b) What time is high tide? What time is low tide?.

8. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Pg. 328 #3 The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled by the sinusoidal function : h(t) = 5 sin[30(t - 5)] + 7 c) What is the depth of the water at 9:00 a.m.?

9. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Pg. 328 #3 The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled by the sinusoidal function : h(t) = 5 sin[30(t - 5)] + 7 d) Find the time during a 24-hr period when the depth of the water is 3m.

10. Lesson 5 – Data Collecting and Modeling Unit 5: Periodic Functions Homework  Pg. 328 #4, 8, 12