91Ó°ÊÓ

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?

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

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

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. $$\csc 0.8$$

Convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. (a) \(-135^{\circ} 36^{\prime \prime} \quad\) (b) \(-408^{\circ} 16^{\prime} 20^{\prime \prime}\)

Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(240.6^{\circ}\) (b) \(-145.8^{\circ}\)

determine whether the statement is true or false. Justify your answer. Because \(\sin (-t)=-\sin t,\) the sine of a negative angle is a negative number.

A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 3.5 feet from its low point to its high point (see figure), and it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy where the high point corresponds to the time \(t=0\) (figure cannot copy)

Finding the Central Angle Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an are of length \(s\). \(r=80\) kilometers, \(s=150\) kilometers

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. $$d=\frac{1}{64} \sin 792 \pi t$$