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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?

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 P.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.

A privately owned yacht leaves a dock in Myrtle Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S \(1.4^{\circ}\) 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?

A ship is 45 miles east and 30 miles south of port. The captain wants to sail directly to port. What bearing should be taken?

Find the length of the sides of a regular pentagon inscribed in a circle of radius 25 inches.

Use the properties of inverse trigonometric functions to evaluate the expression. $$\tan (\arctan 45)$$

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by \(y(t)=\frac{1}{4} e^{-t} \cos 6 t\) where \(y\) is the displacement (in feet) and \(t\) is the time (in seconds). (a) Complete the table. $$\begin{array}{|c|c|c|c|c|c|}\hline t & 0 & \frac{1}{4} & \frac{1}{2} & \frac{3}{4} & 1 \\\\\hline y & & & & & \\\\\hline\end{array}$$ (b) Use the table feature of a graphing utility to approximate the time when the weight reaches equilibrium. (c) What appears to happen to the displacement as \(t\) increases?

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.

Sketch the graph of the function. (Include two full periods.) $$y=\sin \left(x-\frac{\pi}{2}\right)$$

Determine whether the statement is true or false. Justify your answer. The real number 0 corresponds to the point (0,1) on the unit circle.