Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 157: 46

Answer

Refer to the graph below.

Work Step by Step

The parent function of $y=2-3\cos{x}$ is $y=\cos{x}$. The parent function $y=\cos{x}$ has a period of $2\pi$ so one period of its graph is in the interval $[0, 2\pi]$. Dividing this interval into four equal parts yield the key x-values $0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$ and $2\pi$. To graph the given function, perform the following steps: (1) Create a table of values for $y=2-3\cos{x}$ using the key x-values listed above. (Refer to the table below.) (2) Plot each point from the table of values and connect them using a sinusoidal curve to complete one period in the interval $[0, 2\pi]$. (3) Extend the graph one more period by repeating the cycle in the interval $[2\pi, 4\pi]$. Refer to the graph in the answer part above.
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