7.1E: Angles (Exercises)
For the following exercises, convert the angle measures to degrees.
1. \(\frac{\pi}{4}\)
2. \(-\frac{5 \pi}{3}\)
For the following exercises, convert the angle measures to radians.
3. \(-210^{\circ}\)
4. \(180^{\circ}\)
5. Find the length of an arc in a circle of radius 7 meters subtended by the central angle of \(85^{\circ}\).
6. Find the area of the sector of a circle with diameter 32 feet and an angle of \(\frac{3 \pi}{5}\) radians.
For the following exercises, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle.
7. \(420^{\circ}\)
8. \(-80^{\circ}\)
For the following exercises, find the angle between 0 and \(2 \pi\) in radians that is coterminal with the given angle.
9. \(-\frac{20 \pi}{11}\)
10. \(\frac{14 \pi}{5}\)
For the following exercises, draw the angle provided in standard position on the Cartesian plane.
11. \(-210^{\circ}\)
12. \(75^{\circ}\)
13. \(\frac{5 \pi}{4}\)
14. \(-\frac{\pi}{3}\)
15. Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour. Round to the nearest hundredth.
16. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour? Round to the nearest hundredth.