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# 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.

7.1E: Angles (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.