Trigonometry (10th Edition)

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

Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 143: 8

Answer

C

Work Step by Step

The standard form of the equation involving a cos function is $y=a\cos bx$. Comparing $y=2\cos x$ to the standard form, we find that $a=2$ and $b=1$. Since $a=2$, the amplitude of the function is 2. Also, Using the formula $\frac{2\pi}{b}$, we find that the period of $y=2\cos x$ is: $\frac{2\pi}{b}=\frac{2\pi}{1}=2\pi$ Therefore, we need to find a cos wave whose amplitude is 2 and whose period is $2\pi$. We find that graph of option C is the correct answer in this regard.
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