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Chapter 6: Q. 102 (page 412)

Explain the term period as it relates to the graph of a sinusoidal function.

Short Answer

Expert verified

The term period represents the value after which the graph of a sinusoidal function starts repeating itself.

Step by step solution

01

Step 1. Concept Used

If ω>0, then the amplitude and period of y=Asin(ωx)and y=Acos(ωx)are given by

Amplitude=A

Period=2πω

02

Step 2. Find what period represents

The period of a cyclic function gives the x values after which the function starts repeating.

Sinusoidal functions of the form y=Asin(ωx)or y=Acos(ωx)where ω>0are cyclic functions and their period is denoted as T=2πω.

This means that the sinusoidal functions will start repeating after every 2πω, and its one cycle is given by the interval0,2πω.

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