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Example Questions
Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function
What is the amplitude of ?
For any equation in the form , the amplitude of the function is equal to
.
In this case, and
, so our amplitude is
.
Example Question #1 : Find The Amplitude Of A Sine Or Cosine Function
What is the amplitude of ?
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:
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.
For the sine function
where
the amplitude is given as .
As such the amplitude for the given function
is
.
Example Question #1 : Understanding Period And Amplitude
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 .
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.
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