# Precalculus : Find the Amplitude of a Sine or Cosine Function

## Example Questions

### Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function

What is the amplitude of ?      Explanation:

For any equation in the form , the amplitude of the function is equal to .

In this case, and , so our amplitude is .

### Example Question #2 : Find The Amplitude Of A Sine Or Cosine Function

What is the amplitude of ?     Explanation:

The formula for the amplitude of a sine function is from the form: .

In our function, .

Therefore, the amplitude for this function is .

### Example Question #3 : Find The Amplitude Of A Sine Or Cosine Function

Find the amplitude of the following trig function:       Explanation:

Rewrite so that it is in the form of:  The absolute value of is the value of the amplitude. ### Example Question #4 : Find The Amplitude Of A Sine Or Cosine Function

Find the amplitude of the function.      Explanation:

For the sine function where the amplitude is given as .

As such the amplitude for the given function is .

### Example Question #85 : Functions And Graphs

Which of the given functions has the greatest amplitude?      The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is . 