91Ó°ÊÓ

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=14^{\circ}, r=3.0 \mathrm{ft} $$

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. $$ \csc \theta=\sqrt{2}, 0 \leq \theta \leq 2 \pi $$

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. $$ \csc \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi $$

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. $$ r=12 \mathrm{~m}, \omega=\frac{3 \pi \mathrm{rad}}{2 \mathrm{sec}}, t=100 \mathrm{sec} $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=22.8^{\circ}, r=2.6 \mathrm{mi} $$

$$ \text { In Exercises 45-50, convert each angle measure from degrees to radians. Round answers to three significant digits. } $$ $$ 112^{\circ} $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=60^{\circ}, r=15 \mathrm{~km} $$

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. $$ r=6.5 \mathrm{~cm}, \omega=\frac{2 \pi \mathrm{rad}}{15 \mathrm{sec}}, t=50.5 \mathrm{~min} $$

$$ \text { In Exercises 45-50, convert each angle measure from degrees to radians. Round answers to three significant digits. } $$ $$ 172^{\circ} $$

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. $$ \sec \theta \text { is undefined, } 0 \leq \theta \leq 2 \pi $$