91Ó°ÊÓ

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 \(\omega\). $$ \omega=\frac{2 \pi \mathrm{rad}}{3 \mathrm{sec}}, r=9 \mathrm{in} $$

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. $$ \sin \theta=\frac{\sqrt{3}}{2}, 0 \leq \theta \leq 2 \pi $$

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. $$ \theta=11^{\circ}, r=2200 \mathrm{~km} $$

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 \(\omega\). $$ \omega=\frac{3 \pi \mathrm{rad}}{4 \mathrm{sec}}, r=8 \mathrm{~cm} $$

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. $$ \cos \theta=\frac{1}{2}, 0 \leq \theta \leq 2 \pi $$

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. $$ \theta=57^{\circ}, r=22 \mathrm{ft} $$

$$ \text { In Exercises } 25-38 \text {, convert each angle measure from radians to degrees. } $$ $$ \frac{19 \pi}{20} $$

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 \(\omega\). $$ \omega=\frac{\pi \mathrm{rad}}{20 \mathrm{sec}}, r=5 \mathrm{~mm} $$

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. $$ \theta=127^{\circ}, r=58 \mathrm{in} $$

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. $$ \sin \theta=-\frac{1}{2}, 0 \leq \theta \leq 2 \pi $$