Chapter 4.5, Problem 2E

To determine

To fill : the blank space with appropriate term

Answer to Problem 2E

The $\underset{\_}{\boxed{AMPLITUDE}}$ of a sine or cosine curve represents half the distance between the maximum and minimum values of the function.

Explanation of Solution

Given information : The $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ of a sine or cosine curve represents half the distance between the maximum and minimum values of the function.

Concept Involved:

Amplitude: The constant factor $a$ in $y=a\sin x$ and $y=a\cos x$ as a scaling factor − a vertical stretch or vertical shrink of the basic curve. When $\left|a\right|>1,$ the basic curve is stretched, and when $0<\left|a\right|<1,$ the basic curve is shrunk. The result is that the graphs of $y=a\sin x$ and $y=a\cos x$ range between $–a$ and $a$ instead of between $-1$ and $1$ . The absolute value of $a$ is the amplitude of the function. The range of the function for $a>0$ is $-a\le y\le a$ .

The amplitude of $y=a\sin x$ and $y=a\cos x$ represents half the distance between the maximum and the minimum values of the function and is given by $Amplitude=\left|a\right|$ .