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Chapter 4: Problem 7
Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). (TABLE CAN NOT COPY)
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Music and mathematics have been linked over the centuries. Group members should research and present a seminar to the class on music and mathematics. Be sure to include the role of trigonometric functions in the music- mathematics link.
The number of hours of daylight, \(H,\) on day \(t\) of any given year (on January \(1, t=1\) ) in Fairbanks, Alaska, can be modeled by the function $$H(t)=12+8.3 \sin \left[\frac{2 \pi}{365}(t-80)\right]$$ a. March \(21,\) the 80 th day of the year, is the spring equinox. Find the number of hours of daylight in Fairbanks on this day. b. June \(21,\) the 172 nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in Fairbanks on this day. c. December \(21,\) the 355 th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. Find, to the nearest tenth of an hour, the number of hours of daylight in Fairbanks on this day.
Use the exponential growth model, \(A=A_{0} e^{k t},\) to solve this exercise. In \(1980,\) the elderly U.S. population ( 65 and older) was 25.5 million. By \(2010,\) it had grown to 40.3 million. a. Find an exponential growth function that models the data for 1980 through 2010 . b. By which year, to the nearest year, will the elderly U.S. population reach 80 million?
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 \(y=2^{-x} \sin x ?\)
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