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Chapter 4: Problem 24
Convert each angle in radians to degrees. $$\frac{3 \pi}{4}$$
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The average monthly temperature, \(y,\) in degrees Fahrenheit, for Juneau, Alaska, can be modeled by \(y=16 \sin \left(\frac{\pi}{6} x-\frac{2 \pi}{3}\right)+40,\) where \(x\) is the month of the year \(\quad\) (January \(=1,\) February \(=2, \ldots\) December \(=12\) ). Graph the function for \(1 \leq x \leq 12 .\) What is the highest average monthly temperature? In which month does this occur?
Find \(\frac{x}{y}\) for \(x=-\frac{1}{2}\) and \(y=\frac{\sqrt{3}}{2},\) and then rationalize the denominator.
Solve: \(\quad \log _{2}(2 x+1)-\log _{2}(x-2)=1\) (Section 3.4, Example 7)
Repeat Exercise 109 for data of your choice. The data can involve the average monthly temperatures for the region where you live or any data whose scatter plot takes the form of a sinusoidal function.
In Chapter \(5,\) we will prove the following identities: $$ \begin{aligned} \sin ^{2} x &=\frac{1}{2}-\frac{1}{2} \cos 2 x \\ \cos ^{2} x &=\frac{1}{2}+\frac{1}{2} \cos 2 x \end{aligned} $$ Use these identities to solve. Use the identity for \(\cos ^{2} x\) to graph one period of \(y=\cos ^{2} x\)
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