# 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 ?

Possible Answers:

Correct answer:

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 ?

Possible Answers:

Correct answer:

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

Find the amplitude of the following trig function:

Possible Answers:

Correct answer:

Explanation:

Rewrite  so that it is in the form of:

The absolute value of  is the value of the amplitude.

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

Find the amplitude of the function.

Possible Answers:

Correct answer:

Explanation:

For the sine function

where

the amplitude is given as  .

As such the amplitude for the given function

is

.

### Example Question #1 : Period And Amplitude

Which of the given functions has the greatest amplitude?

Possible Answers:

Correct answer:

Explanation:

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 .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.