Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 149: 32

Answer

Refer to the gaph below.
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Work Step by Step

RECALL: The functions $y=a \cdot \sin{bx}$ and $y=a \cdot \cos{bx}$ have: period = $\dfrac{2\pi}{b}$ amplitude = $|a|$ The given function has $a=-5$ and $b=2$ thus period = $\dfrac{2\pi}{2}=\pi$ amplitude = $|-5| = 5$ To graph the function, perform the following steps: (1) With a period of $\pi$, one period of the function is over the interval $[0, \pi]$. (2) Divide this interval into four parts to obtain the x-values $0, \frac{1}{4}\pi, \frac{1}{2}\pi, \frac{3}{4}\pi, \text{ and } \pi$. (3) Make a table of values using the x-values above. (Refer to the table below.) (4) Plot the five points of the table of values then connect them using a sinusoidal curve whose ampliude is $5$. (5) Repeat the cycle of the graph form one more period, which is $[\pi, 2\pi]$. (Refer to the graph in the answer part above.)
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