7.1E: Angles (Exercises)

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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.