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Chapter 4: Problem 62
Use a calculator to find the value of the trigonometric function to four decimal places. $$\cos 0.6$$
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Use a vertical shift to graph one period of the function. $$y=\sin x+2$$
The following figure shows the depth of water at the end of a boat dock. The depth is 6 feet at low tide and 12 feet at high tide. On a certain day, low tide occurs at 6 A.M. and high tide at noon. If \(y\) represents the depth of the water \(x\) hours after midnight, use a cosine function of the form \(y=A \cos B x+D\) to model the water's depth.
The number of hours of daylight in Boston is given by $$ y=3 \sin \frac{2 \pi}{365}(x-79)+12 $$ where \(x\) is the number of days after January 1 a. What is the amplitude of this function? b. What is the period of this function? c. How many hours of daylight are there on the longest day of the year? d. How many hours of daylight are there on the shortest day of the year? e. Graph the function for one period, starting on January 1
will help you prepare for the material covered in the next section.
$$\text { Solve: } \quad-\frac{\pi}{2}
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 \(y=2^{-x} \sin x ?\)
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