7.1E: Angles (Exercises)

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Dec 26, 2024
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- 7.1: Angles
- 7.2: Right Triangle Trigonometry

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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.

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