Question

which of the following statements describes the definition of amplitude of a sine or cosine function?
choose the correct answer.
a. the amplitude is the measure of half the distance between the maximum and minimum values.
b. the amplitude measures the distance between the maximum and minimum values.
c. the amplitude is the minimum value of the sine or cosine function.
d. the amplitude is the maximum value of the sine or cosine function.

Explanation:

The amplitude of a sine or cosine function is defined as half the distance between the maximum and minimum values of the function. For a standard function $y = A\sin(x)$ or $y = A\cos(x)$, if the max value is $|A|$ and min is $-|A|$, the distance between them is $2|A|$, so half that distance is $|A|$, which is the amplitude. Options B, C, D do not match this definition.

Answer:

A. The amplitude is the measure of half the distance between the maximum and minimum values.