Lesson 8B: Solving Problems Using Sinusoidal Functions

The ocean waves you see and hear when you visit one of Canada's three coasts can be very relaxing or extremely scary. Your reaction might depend on whether you are watching them or trying to keep your boat from succumbing to them.

The depth of water in harbours is of tremendous importance to ship owners. They study tide tables and depth charts to be sure that their ships can travel safely in and out of the ports. Scientists who study tides make computer-generated, sinusoidal-type graphs of the tide level versus time.

Many times, using a sinusoidal function allows one to make predictions that are extremely useful. In fact, many computer programs that predict tides use multiple sine waves in calculating their results. Anything that has a regular cycle such as tides, temperatures, or rotation of the earth can be modelled using a sine or cosine function. However, when using technology such as computer programs or graphing calculator, typically a sine curve of the form y = a sin(bx + c) + d is fitted to the data.

By the end of this lesson, you should be able to

	graph data and determine the sinusoidal function that best fits the data
	interpret the graph of a sinusoidal function that models a situation, and explain your reasoning
	use technology to solve a problem that involves data best modelled by a sinusoidal function