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Chapter 4: Problem 55
A tower that is 125 feet tall casts a shadow 172 feet long. Find the angle of elevation of the Sun to the nearest degree. (IMAGE CANNOT COPY)
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Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$50.42^{\circ}$$
For \(x>0,\) what effect does \(2^{-x}\) in \(y=2^{-x} \sin x\) have on the graph of \(y=\sin x ?\) What kind of behavior can be modeled by a function such as \(y=2^{-x} \sin x ?\)
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 \(g\) $$f(x)=\cos x, g(x)=\sin 2 x, h(x)=(f-g)(x)$$
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 \(y=\cos ^{2} x\)
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.
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