## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 162: 43

#### Answer

Refer to the graph below. #### Work Step by Step

RECALL: The graph of $y=a \cdot \sin{[b(x-d)]}$ has: amplitude = $|a|$ period = $\frac{2\pi}{b}$ phase shift = $|d|$, to the left when $d\lt0$, to the right when $d\gt0$ The given function has: $a=\frac{3}{2}$ $b=2$ $d=-\frac{\pi}{4}$ Thus, the given function has: amplitude = $\frac{3}{2}$ period = $\frac{2\pi}{2} = \pi$ phase shift = $|-\frac{\pi}{4}|=\frac{\pi}{4}$ to the left Therefore, the graph of the given function has the following properties/characteristics: amplitude = $\frac{3}{2}$ so the y-values range from $-\frac{3}{2}$ to $\frac{3}{2}$ phase shift = $\frac{\pi}{4}$ units to the left one period interval = $[-\frac{\pi}{4}, \frac{3\pi}{4}]$ Refer to the graph in the answer part above.

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