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Chapter 4: Problem 90
What is the amplitude of the sine function? What does this tell you about the graph?
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Solve: \(\quad 8^{x+5}=4^{x-1}\) (Section 3.4, Example 1)
Rounded to the nearest hour, Los Angeles averages 14 hours of daylight in June, 10 hours in December, and 12 hours in March and September. Let \(x\) represent the number of months after June and let \(y\) represent the number of hours of daylight in month \(x .\) Make a graph that displays the information from June of one year to June of the following year.
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 \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)
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 \(g\) $$f(x)=\cos x, g(x)=\sin 2 x, h(x)=(f-g)(x)$$
Use a vertical shift to graph one period of the function. $$y=\cos x+3$$
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