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Chapter 4: Problem 22
Use a calculator to evaluate the expression. Round your result to two decimal places. $$\arcsin 0.65$$
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A ship leaves port at noon and has a bearing of \(\mathrm{S} 29^{\circ} \mathrm{W}\). The ship sails at 20 knots. (a) How many nautical miles south and how many nautical miles west will the ship have traveled by 6: 00 P.M.? (b) At 6: 00 e.m., the ship changes course to due west. Find the ship's bearing and distance from the port of departure at 7: 00 P.M.
Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow 1^{-}, \text {the value of } \arcsin x \rightarrow \text{______}$$
Find the length of the sides of a regular hexagon inscribed in a circle of radius 25 inches.
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. $$d=\frac{1}{64} \sin 792 \pi t$$
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? $$f(t)=4 \cos \pi t+3 \sin \pi t$$
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