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Unit 3Sinusoidal Functions

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Types of FunctionsLinear:

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Absolute Value

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Quadratic

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Sinusoidal Function

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Domain/Range

Domain: the set of possible x-valuesRange: the set of possible y-values

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Function:

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Periodic BehaviourAny function is called periodic if it “repeats” itself on intervals of any fixed length. For example the sine curve. 

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A special type of periodic function is called a sinusoidal function.

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How to Determine if a Function is Sinusoidal

A sinusoidal graph has:1. Only one maximum and one minimum in each periodic

interval.

2. A sinusoidal axis (a horizontal line halfway between the maximum and the minimum).

3. A common amplitude value (the distance from the sinusoidal axis to the maximum or minimum).

sinusoidal axis

maximum

minimum minimum

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Is this graph periodic and sinusoidal?Explain.

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Is this graph periodic and sinusoidal?Explain.

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Is this graph periodic and sinusoidal?Explain.

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Is this graph periodic and sinusoidal?Explain.

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Is this graph periodic and sinusoidal?Explain.

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Is this graph periodic and sinusoidal?Explain.

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Page 72 Workbook

The motion of a Ferris wheel can be represented by a sinusoidal function.

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Identify and label the key characteristics of this graph.

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Remember : velocity = distance ÷ time

distance around a wheel = 2πr (circumference of a circle)

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Maximum Height

Minimum Height

Revolution

Axle Height

Radius

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Maximum Height

Minimum Height

Revolution

Axle Height

Radius