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Chapter 4: Problem 111

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing one complete cycle of \(y=A \sin (B x-C)\) I find it easiest to begin my graph on the \(x\) -axis.

Short Answer

Expert verified
The statement makes sense. This is because one complete cycle of a sine wave indeed starts and finishes on the x-axis.

Step by step solution

01

Understanding Parameters

Recall the sine function, \(y=A \sin (Bx-C)\), where 'A' is the amplitude, 'B' affects the period, and 'C' shifts the graph left or right. A complete cycle of a sine wave begins and ends on the x-axis and passes through two key points: the peak and the trough.
02

Analyzing the Statement

The given statement suggests starting the graph of a sine function on the x-axis. This makes sense because a complete cycle of the sine function indeed starts and finishes on the x-axis.
03

Visualizing a Sine Wave

For a sine wave, if we start our graph at the origin (0,0), we are effectively graphing the function \(y=\sin(x)\). The sine function begins and ends at (0,0) for one complete cycle, provided there are no horizontal or vertical shifts. Hence, beginning the graph on the x-axis for a complete cycle of a sine function is a valid approach.

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