## 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: 58

#### Answer

Refer to the graph below.

#### Work Step by Step

Write the given equation in the form $y=c+a\cdot \cos{[b(x-d)]}$ to obtain: $y=4+[-3\cos{(x-\pi)}]$ Find one interval of the given function whose length is one period: \begin{array}{ccccc} &0 &\le &x-\pi&\le &2\pi \\&0+\pi &\le &x-\pi+\pi &\le &2\pi+\pi \\&\pi &\le &x &\le &3\pi \end{array} Thus, one interval of the given function is $[\pi, 3\pi]$. Dividing this interval into four equal parts yield the key x-values $\pi, \frac{3\pi}{2}, 2\pi, \frac{5\pi}{2},$ and $3\pi$. To graph the given function, perform the following steps: (1) Create a table of values for the function $y=4+[-3\cos{\left(x-\pi\right)}]$ using the key x-values listed above. (Refer to the table below.) (2) Plot each point in the table then connect them using a sinusoidal curve. (Refer to the attached graph in the answer part above.)

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