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1.) In nature, Sinusoidal Functions can be used to measure the tidal change of large bodies of water. 

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1.) In nature, Sinusoidal Functions can be used to measure the tidal change of large bodies of water. 

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2.) In order to find the period of the function that determines the tidal changes, one must first find the period of the tidal changes. For example, in Boston, MA, the tide comes in, goes all the way out, and then comes back in again in a period of about 12 hours. 

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2.) In order to find the period of the function that determines the tidal changes, one must first find the period of the tidal changes. For example, in Boston, MA, the tide comes in, goes all the way out, and then comes back in again in a period of about 12 hours. 

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3.) The period of a typical sine wave is 2π. When we divide 2π by 12 hours, we end up with a new period of π/6. 

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3.) The period of a typical sine wave is 2π. When we divide 2π by 12 hours, we end up with a new period of π/6. 

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5.) To find the amplitude of the function, we have to look at how far the tide will come in and how far the tide will go out. In this case, the tide comes in about 4.8 feet both above and below the midline. 

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5.) To find the amplitude of the function, we have to look at how far the tide will come in and how far the tide will go out. In this case, the tide comes in about 4.8 feet both above and below the midline. 

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4.) A phase shift of 3 is then added to the graph. We do this because the tide changes 3 times in the 12-hour period, thus the graph needs a phase shift to reflect that. 

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4.) A phase shift of 3 is then added to the graph. We do this because the tide changes 3 times in the 12-hour period, thus the graph needs a phase shift to reflect that. 

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7.) Here is one period (12-hours of tidal changes) of our graph. As shown below, our midline is 5.1, and there is a total of 3 tide changes in the 12-hour period. 

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7.) Here is one period (12-hours of tidal changes) of our graph. As shown below, our midline is 5.1, and there is a total of 3 tide changes in the 12-hour period. 

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6.) Finally, we add 5.1 to the end of the graph for a vertical translation. 5.1 is the average height of the tides. 

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6.) Finally, we add 5.1 to the end of the graph for a vertical translation. 5.1 is the average height of the tides. 

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Here is the graph for the second example. 

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Here is the graph for the second example. 

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Here is another example of sinusoids being used to represent ocean tides. 

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Here is another example of sinusoids being used to represent ocean tides. 

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(Sorry it's sideways)

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https://www.dummies.com/education/math/trigonometry/measure-tidal-change-using-a-trigonometry-graph/

http://mathforum.org/library/drmath/view/54163.html