91Ó°ÊÓ

In Exercises 25-36, use a calculator to approximate the length of each arc made by the indicated central angle and radius of each circle. Round answers to two significant digits. $$ \theta=127^{\circ}, r=58 \mathrm{in} $$

$$ \text { In Exercises } 25-38 \text {, convert each angle measure from radians to degrees. } $$ $$ \frac{13 \pi}{36} $$

In Exercises 33-42, find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius \(r\) and angular speed \(\omega\). $$ \omega=\frac{4 \pi \mathrm{rad}}{15 \mathrm{sec}}, r=2.5 \mathrm{in} $$

$$ \text { In Exercises } 25-38 \text {, convert each angle measure from radians to degrees. } $$ $$ -\frac{7 \pi}{15} $$

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. $$ \cos \theta=-\frac{\sqrt{2}}{2}, 0 \leq \theta \leq 2 \pi $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=\frac{\pi}{6}, r=7 \mathrm{ft} $$

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

In Exercises 33-42, find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius \(r\) and angular speed \(\omega\). $$ \omega=\frac{8 \pi \mathrm{rad}}{15 \mathrm{sec}}, r=4.5 \mathrm{~cm} $$

$$ \text { In Exercises } 25-38 \text {, convert each angle measure from radians to degrees. } $$ $$ -\frac{8 \pi}{9} $$

In Exercises \(37-48\), find the area of the circular sector given the indicated radius and central angle. Round answers to three significant digits. $$ \theta=\frac{\pi}{5}, r=3 \text { in. } $$