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Chapter 4: Problem 27
Convert each angle in radians to degrees. $$-3 \pi$$
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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. a. Graph \(y=\sin x\) for \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\) b. Based on your graph in part (a), does \(y=\sin x\) have an inverse function if the domain is restricted to \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] ?\) Explain your answer. c. Determine the angle in the interval \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) whose sine is \(-\frac{1}{2} .\) Identify this information as a point on your graph in part (a).
Describe a relationship between the graphs of \(y=\sin x\) and \(y=\cos x\)
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. $$30.42^{\circ}$$
Use a graphing utility to graph two periods of the function. $$y=0.2 \sin \left(\frac{\pi}{10} x+\pi\right)$$
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