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Chapter 4: Problem 30
Use a calculator to evaluate the expression. Round your result to two decimal places. $$\arcsin (-0.125)$$
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Is a degree or a radian the greater unit of measure? Explain.
A privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of \(S 1.4^{\circ} \mathrm{E}\) The yacht averages a speed of 20 knots over the 428 -nautical-mile trip. (a) How long will it take the yacht to make the trip? (b) How far east and south is the yacht after 12 hours? (c) A plane leaves Myrtle Beach to fly to Freeport. What bearing should be taken?
Use a graphing utility to graph the function. $$f(x)=\pi \arcsin (4 x)$$
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? $$f(t)=4 \cos \pi t+3 \sin \pi t$$
Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\sin ^{2} x, \quad g(x)=\frac{1}{2}(1-\cos 2 x)$$
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