Chapter 14

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. The hour hand of a clock is 85.5 mm long. How far does the tip of the hand travel between 1: 00 A.M. and 11: 00 A.M.?

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$130^{\circ}$$

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. Find the radius of a circular railroad track that will cause a train to change direction by \(17.5^{\circ}\) in a distance of \(180 \mathrm{m}\).

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$66^{\circ}$$

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. The pulley attached to the tuning knob of a radio (Fig. \(14-13\) ) has a radius of \(35 \mathrm{mm}\). How far will the necdle move if the knob is turned a quarter of a revolution?

A milling machine cutter has a diameter of \(75.0 \mathrm{mm}\) and is rotating at 56.5 rev/min. What is the linear speed at the edge of the cutter?

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$240^{\circ}$$

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. One circular "track" on a magnetic disk used for computer data storage is located at a radius of 155 mm from the center of the disk. If 1000 "bits" of data can be stored in \(1 \mathrm{mm}\) of this track, how many bits can be stored in the length of this track subtending an angle of \(\pi / 12\) rad?

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$126^{\circ}$$

You are programming a numerically controlled drill press to drill holes in a cast iron block, whose recommended cutting speed is \(30.0 \mathrm{m} / \mathrm{min}\). What rotational speed of a 25.4 mm diameter drill will give that cutting speed?

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. If we assume the earth's orbit around the sun to be circular, with a radius of 93 million mi, how many miles does the earth travel (around the sun) in 125 days?

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$105^{\circ}$$

Writing: When we multiply an angular velocity in radians per second by length in feet, we get a linear speed in feet per second. Explain why radians do not appear in the units for linear speed.

Where needed, assume the earth to be a sphere with a radius of 3960 mi. Actually, the distance from pole to pole is about 27 mi less than the diameter at the equator. A 1.25 -m-long pendulum swings \(5.75^{\circ}\) on each side of the vertical. Find the length of arc traveled by the end of the pendulum.

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$78^{\circ}$$

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$305^{\circ}$$

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$400^{\circ}$$

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$150^{\circ}$$

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$81^{\circ}$$

Convert each angle given in degrees to radian measure in terms of \(\pi\) $$189^{\circ}$$

A circular highway curve has a radius of \(325.500 \mathrm{ft}\) and a central angle of \(15^{\circ} 25^{\prime} 05^{\prime \prime}\) measured to the centerline of the road. Find the length of the curve.

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{\pi}{8}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{2 \pi}{3}$$

Earlier we gave the formula for the area of a circular sector of radius \(r\) and central angle \(\theta:\) area \(=r^{2} \theta / 2\) (Eq. 77 ). Using Eq. \(76, \theta=s / r,\) show that the area of a sector is also equal to \(r s / 2,\) where \(s\) is the length of the arc intercepted by the central angle.

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{9 \pi}{11}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{3 \pi}{5}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{\pi}{9}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{4 \pi}{5}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{7 \pi}{8}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{5 \pi}{9}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{2 \pi}{15}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{6 \pi}{7}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{\pi}{12}$$

Convert each angle given in radian measure to degrees. Give approximate values to one decimal place. $$\frac{8 \pi}{9}$$

Evaluate to four significant digits. $$\sin \frac{\pi}{3}$$

Evaluate to four significant digits. $$\tan 0.442$$

Evaluate to four significant digits. $$\cos 1.063$$

Evaluate to four significant digits. $$\tan \left(-\frac{2 \pi}{3}\right)$$

Evaluate to four significant digits. $$\cos \frac{3 \pi}{5}$$

Evaluate to four significant digits. $$\sin \left(-\frac{7 \pi}{8}\right)$$

Evaluate to four significant digits. $$\sec 0.355$$

Evaluate to four significant digits. $$\csc \frac{4 \pi}{3}$$

Evaluate to four significant digits. $$\cot \frac{8 \pi}{9}$$

Evaluate to four significant digits. $$\tan \frac{9 \pi}{11}$$

Evaluate to four significant digits. $$\cos \left(-\frac{6 \pi}{5}\right)$$

Evaluate to four significant digits. $$\sin 1.075$$

Evaluate to four significant digits. $$\cos 1.832$$

Evaluate to four significant digits. $$\cot 2.846$$

Evaluate to four significant digits. $$\sin 0.6254$$

Evaluate to four significant digits. $$\arcsin 0.7263$$