91Ó°ÊÓ

In Exercises 31-50, use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$ \cot \theta=1,0 \leq \theta \leq 2 \pi $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=27^{\circ}, r=2.5 \mathrm{~mm} $$

$$ \text { In Exercises 39-44, convert each angle measure from radians to degrees. Round answers to the nearest hundredth of a degree. } $$ $$ -5.9841 $$

In Exercises 43-52, find the distance a point travels along a circle \(s\), over a time \(t\), given the angular speed \(\omega\), and radius of the circle \(r\). Round to three significant digits. $$ r=2 \mathrm{~mm}, \omega=6 \pi \frac{\mathrm{rad}}{\mathrm{sec}}, t=11 \mathrm{sec} $$

In Exercises 43-52, find the distance a point travels along a circle \(s\), over a time \(t\), given the angular speed \(\omega\), and radius of the circle \(r\). Round to three significant digits. $$ r=5.2 \text { in., } \omega=\frac{\pi \mathrm{rad}}{15 \mathrm{sec}}, t=10 \mathrm{~min} $$

In Exercises 31-50, use the unit circle to find all of the exact values of \(\theta\) that make the equation true in the indicated interval. $$ \sec \theta=-\sqrt{2}, 0 \leq \theta \leq 2 \pi $$

$$ \text { In Exercises 45-50, convert each angle measure from degrees to radians. Round answers to three significant digits. } $$ $$ 47^{\circ} $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=1.2^{\circ}, r=1.5 \mathrm{ft} $$

In Exercises 43-52, find the distance a point travels along a circle \(s\), over a time \(t\), given the angular speed \(\omega\), and radius of the circle \(r\). Round to three significant digits. $$ r=3.2 \mathrm{ft}, \omega=\frac{\pi \mathrm{rad}}{4 \mathrm{sec}}, t=3 \mathrm{~min} $$

$$ \text { In Exercises 45-50, convert each angle measure from degrees to radians. Round answers to three significant digits. } $$ $$ 65^{\circ} $$