Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the significance of the period in trigonometric graphs?

1. It determines the maximum value of the function

2. It represents the distance between two consecutive peaks

3. It indicates the rate of change of the function

4. It shows the amplitude of the wave

The correct answer is: It represents the distance between two consecutive peaks

The significance of the period in trigonometric graphs is that it represents the distance between two consecutive peaks, or more generally, the length of one complete cycle of the wave. This means that if you look at the graph of a sine, cosine, or tangent function, the period tells you how far along the x-axis you must go to see the function repeat itself. For instance, the sine and cosine functions have a period of \(2\pi\); after \(2\pi\) units, the values of these functions will repeat. Understanding the period is crucial for analyzing the behavior of trigonometric functions, as it helps in predicting the values of the function at various points and in applications such as waves, oscillations, and harmonic motions. While other aspects such as amplitude and rate of change are important for understanding trigonometric graphs, they do not pertain directly to the concept of periodicity. The maximum value of the function and the amplitude refer to the height of the peaks rather than the distance between them, and the rate of change relates to how rapidly the function values are changing at any given point, which is distinct from the periodic distance.