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Chapter 4: Problem 2
Fill in the blanks. The _____ of a sine or cosine curve represents half the distance between the maximum and minimum values of the function.
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Use a graphing utility to graph the function. $$f(x)=\pi \arcsin (4 x)$$
\(\quad\) A point on the end of a tuning fork moves in simple harmonic motion described by \(d=a \sin \omega t .\) Find \(\omega\) given that the tuning fork for middle C has a frequency of 264 vibrations per second.
For the simple harmonic motion described by the trigonometric function, find (a) the maximum displacement, (b) the frequency, (c) the value of \(d\) when \(t=5,\) and (d) the least positive value of \(t\) for which \(d=0 .\) Use a graphing utility to verify your results. $$d=\frac{1}{4} \sin 6 \pi t$$
Angle of Elevation The height of an outdoor basketball backboard is \(12 \frac{1}{2}\) feet, and the backboard casts a shadow \(17 \frac{1}{3}\) feet long. A. Draw a right triangle that gives a visual representation of the problem. Label the known and unknown quantities. B. Use a trigonometric function to write an equation involving the unknown angle of elevation. C. Find the angle of elevation of the sun.
Consider the functions \(f(x)=\sin x\) and \(f^{-1}(x)=\arcsin x\). (a) Use a graphing utility to graph the composite functions \(f \circ f^{-1}\) and \(f^{-1} \circ f\). (b) Explain why the graphs in part (a) are not the graph of the line \(y=x .\) Why do the graphs of \(f \circ f^{-1}\) and \(f^{-1}\) o \(f\) differ?
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