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Chapter 4: Problem 114

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A ride on a circular Ferris wheel is like riding sinusoidal graphs.

Short Answer

Expert verified
The statement that a ride on a circular Ferris wheel is like riding sinusoidal graphs does make sense. It is because of the cyclical and continuous behavior, that both, a ride on Ferris wheel and sinusoids exhibit. In fact, the sinusoidal functions (like cosine or sine) can model the height of a passenger on a Ferris wheel over time.

Step by step solution

01

Understanding characteristics of a Ferris wheel ride

A Ferris wheel moves in continuous, smooth, rotational circular motion. The passengers' height relative to the ground changes systematically with time, and after a complete cycle it repeats itself again. The system is without any interruption and is cyclical.
02

Understanding characteristics of a sinusoidal graph

Sinusoidal functions like sine or cosine functions create a wave-like pattern. It smoothly rises and falls in a continuous repetitive cycle, showing a cyclical behavior. The sinusoidal pattern returns to its initial position after a complete wave, which is similar to a Ferris wheel's cyclical motion.
03

Comparing and Contrasting characteristics

Despite one showing a circular path while the other portrays a wave path, both the Ferris wheel movement and sinusoidal graph exhibit cyclical behavior. This cyclical behavior results from a systematically repeating pattern over time. The height of a passenger on a Ferris wheel as a function of time can be modeled by a sinusoidal function owing to this similarity.

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