Periodic Functions Calculator

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Example

Created on 2024-06-20Asked by Ethan Baker (Solvelet student)

Find the period of the function

f(x) = \sin(3x)

Solution

To find the period of the function

f(x) = \sin(3x)

: 1. The period of the function

f(x) = \sin(ax)

is given by

\frac{2\pi}{|a|}

. 2. Substitute

a = 3

into the formula:

\text{Period} = \frac{2\pi}{|3|} = \frac{2\pi}{3}.

Therefore, the period of the function

f(x) = \sin(3x)

\frac{2\pi}{3}

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Mila Scott on Solvelet

1. Identify the period, amplitude, and phase shift of the function

y = 3\sin(2x - \pi)

.2. Graph one period of the function

f(x) = 4\cos(3x)

over the interval

[0, 2\pi]

DefinitionA periodic function is defined as an activity that repeats its value after a period of time, called a period. If f (x + T) = f (x) for all x and some positive constant T, For example, the sine function sin(x) is periodic with period 2π.

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