91Ó°ÊÓ

Nautical Miles If a central angle with its vertex at the center of the earth has a measure of \(1^{\prime}\), then the arc on the surface of the earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (Figure 16). Clock Through how many radians does the minute hand of a clock turn during a 25 -minute period?

Find the exact value of each of the following. $$ \cos 420^{\circ} $$

Use the unit circle to find all values of \(\theta\) between 0 and \(2 \pi\) for which \(\cot \theta=\sqrt{3}\)

In the problems that follow, point \(P\) moves with angular velocity \(\omega\) on a circle of radius \(r\). In each case, find the distance \(s\) traveled by the point in time \(t\). $$ \omega=15 \mathrm{rad} / \mathrm{sec}, r=5 \mathrm{ft}, t=1 \mathrm{~min} $$

Simplify each expression. $$\pi-\frac{\pi}{3}$$

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of \(\pi / 12\). Trace the circle to find the sine and cosine of each angle to the nearest ten-thousandth. \(\frac{\pi}{4}\)

Find the exact value of each of the following. $$ \cot 480^{\circ} $$

In the problems that follow, point \(P\) moves with angular velocity \(\omega\) on a circle of radius \(r\). In each case, find the distance \(s\) traveled by the point in time \(t\). $$ \omega=10 \mathrm{rad} / \mathrm{sec}, r=6 \mathrm{ft}, t=2 \mathrm{~min} $$

Find the exact value of each of the following. $$ \cot 510^{\circ} $$

Simplify each expression. $$\pi+\frac{\pi}{6}$$