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Chapter 4: Problem 30
Convert each angle in degrees to radians. Round to two decimal places. $$76^{\circ}$$
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Graph one period of each function. $$y=\left|2 \cos \frac{x}{2}\right|$$
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?
Graph one period of each function. $$y=\left|3 \cos \frac{2 x}{3}\right|$$
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 \(y=\cos ^{2} x\)
Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of h by adding or subtracting the corresponding \(y\) -coordinates on the graphs of \(f\) and \(g\) $$f(x)=2 \cos x, g(x)=\cos 2 x, h(x)=(f+g)(x)$$
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