# What is the amplitude of sine and cosine?

## What is the amplitude of sine and cosine?

The amplitude of the sine and cosine functions is the vertical distance between the sinusoidal axis and the maximum or minimum value of the function. In relation to sound waves, amplitude is a measure of how loud something is.

## How do you find the amplitude of a sine function?

The amplitude of y=asin(x) and y=acos(x) represents half the distance between the maximum and minimum values of the function.

How do you write a period with amplitude and cosine?

1. In y=acos(b(x−c))+d :
2. • |a| is the amplitude. • 2πb is the period.
3. The amplitude is 3 , so a=3 .
4. The period is 2π3 , so we solve for b .
5. b=3.
6. The phase shift is +π9 , so c=π9 .
7. The vertical transformation is +4 , so d=4 .
8. ∴ The equation is y=3cos(3(x−π9))+4 , which can be written as y=3cos(3x−π3)+4.

What is the amplitude of cosine function?

Amplitude and Period a Cosine Function The amplitude of the graph of y=acos(bx) is the amount by which it varies above and below the x -axis. Amplitude = | a | The period of a cosine function is the length of the shortest interval on the x -axis over which the graph repeats. Period = 2π|b|

### How do you find the period of a sine wave?

We have a really easy way to determine the period of the sine function. If we have a sine function of the form f(x) = Asin(Bx + C) + D, then the period of the function is 2π / |B|.

What is period and amplitude?

The Period goes from one peak to the next (or from any point to the next matching point): The Amplitude is the height from the center line to the peak (or to the trough).

What is amplitude and period of Sine and cosine functions?

Amplitude and Period of Sine and Cosine Functions. The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function. Amplitude = | a |. Let b be a real number. The period of y = a sin ( b x ) and y = a cos ( b x ) is given by. Period = 2 π | b |. Example:

#### What is the amplitude of Y = a sin (x)?

The amplitude of y = a sin ( x) and y = a cos ( x) represents half the distance between the maximum and minimum values of the function. Let b be a real number. The period of y = a sin ( b x) and y = a cos ( b x) is given by

#### How do you find the period and amplitude of a function?

The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function. Amplitude = | a |. Let b be a real number. The period of y = a sin ( b x ) and y = a cos ( b x ) is given by. Period = 2 π | b |. Example: Find the period and amplitude of y = 5 2 cos ( x 4 ) .

What is the amplitude of sin 4 with period 2π?

So amplitude is 1, period is 2π, there is no phase shift or vertical shift: Example: 2 sin (4 (x − 0.5)) + 3 amplitude A = 2 period 2π/B = 2π/4 = π/2

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