Please create math notes in word (sentences) form explaining the concept of Modeling with Trigonometric Functions and how to solve problems like this (more so general). See attachment for examples of work and what kind of problems.

Unit 2 (Chapter 6): Trigonometric Functions Lesson 2.6: Modelling with Trigonometric Functions Learning Goals: To learn how to model and solve problems that involve trigonometric functions and radian measurement Example 1: The tides change the depth of the water in the harbour. On one day in October, the tides have a high point of approximately 10 m at 2 p.m. and a low point approximately 1.2 m at 8:15 p.m. A particular sailboat has a draft of 2 m. This means that it can only move in water that is at least 2 m deep. Create a sinusoidal function to model the problem, and use it to determine whether the sailboat can exit the harbour safely at 6 p.m. max: 10m at 2p.m. -> += 14h min: 1.2m at 8:15 pm - t= 20h 15 min = 20h+ ish 4 = a cos (k (t-d) ) +c = 20.25 h a = max- min _ 10 - 1.2 - 2 2 - = 4.4 c = max + min _ 10+1.2 - 5.6 2 2 period = 2 x (20.25- 14) = 2(6.25) =12.5 k= 2TT 2 75 4TT 12. 5 25/ 2 25 d = 14 ( since this is when max occurs) 4= 4.4 cos ( (t- 14)) + 5.6 At 6 p.m., t = 18h 4 = 4.4 cos (471 25 ( 18-14) ) + 5.6 = 3.73 m > 2m . . yes, it is safe for the sailboat to exit the harbour at 6 p.m