Write Each Degree Measure in Radians As a Multiple of Π and Each Radian Measure in Degrees

4-2 Practice Degrees and Radians

Write each decimal degree measure in DMS form and each DMS measure in decimal degree form to the nearest thousandth.

1. 28.955 2. –57.3278

3. 32° 28' 10" 4. –73° 14' 35"

Write each degree measure in radians as a multiple of π and each radian measure in degrees.

5. −250° 6. 6° 7. −145°

8. 870° 9. 18° 10. −820°

11. 4π 12. 13. −1

14. 15. −2.56 16. −

Identify all angles that are coterminal with the given angle. Then find and draw one positive and one negative angle coterminal with the given angle.

17. 43° 18. −

Find the length of the intercepted arc with the given central angle measure in a circle of the given radius. Round to the nearest tenth.

19. 30°, r = 8 yd 20. , r = 10 in.

Find the rotation in revolutions per minute given the angular speed and the radius given the linear speed and the rate of rotation.

21. ω = rad/s 22. V = 32 m/s, 100 rev/min

23. ω = 2.7 rad/s 24. ω = π rad/hr NAME ______DATE______PERIOD ______

25. ω = π rad/min 26. V = 24.8 m/s, 120 rev/min

27. V = 118 ft/min , 3.6 rev/s 28. V = 256 in./h, 0.5 rev/min

29. On a game show, a contestant spins a wheel. The angular speed of the wheel was ω = radians per second. If the wheel maintained this rate, what would be the rotation in revolutions per minute?

Find the area of each sector. 30. θ = , r = 14 in. 31. θ = , r = 4 m

32. GARDEN Jayden is planting a circular garden in her backyard that will have a radius of 10 feet, as shown below.

a. What area does she want to use for tomatoes?

b. What area does she want to use for wildflowers?

c. If six ounces of wildflower seeds can cover 10 square feet, how many ounces of seeds does Jayden need to buy in order to plant all of the wildflowers?

33. CLOCK A clock is divided into 12 sectors each with an angle of radians.

a. How many hours pass when the hour hand moves 77π radians?

b. If the clock’s radius is 14 inches, what is the area of the smaller sector formed by the hands at the 5:00 position?

c. What is the angular speed of the hour hand and minute hand?

Chapter 10 2 Glencoe Algebra 2