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Chapter 4: Problem 23
Use a calculator to evaluate the expression. Round your result to two decimal places. $$\arcsin (-0.75)$$
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A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed (in feet per minute) of the platform rim of the carousel.
Write the function in terms of the sine function by using the identity $$A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).$$ Use a graphing utility to graph both forms of the function. What does the graph imply? $$f(t)=4 \cos \pi t+3 \sin \pi t$$
\(\quad\) 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.
Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\sin x-\cos \left(x+\frac{\pi}{2}\right), \quad g(x)=2 \sin x$$
Navigation An airplane flying at 600 miles per hour has a bearing of \(52^{\circ} .\) After flying for 1.5 hours, how far north and how far east will the plane have traveled from its point of departure?
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