Precalculus Name: ______Date: ______Pd: _____ 4.1 Partial Review 1° = 60' or 60 minutes 1 minute = 60 '' or 60 seconds To Convert from DMS to DD: 5° 36'28'' 1. The degree is the whole number, in this case, 5. 36 2. Divide the minutes by 60:  .6000 60 28 3. Divide the seconds by 3600: = .0078 (60)(60) 36 28 ° Or 5 + + = 5.6078° 4. Add 5 + .6000 + .0078 to get 5.6078 60 3600

Answer: 5° 36'28'' = 5.60778°

To Convert from DD to DMS: 28.2472 1. The number left of the decimal is the degrees: 28° 2. Multiply the remaining digits by 60 to find the minutes: .2472 60  14.8332 The 14 represents the minutes amount. 3. Multiply the remaining digits by 60 to find the seconds: .8332 60  49.9920 Round up to the nearest ones place, in this case 50. This represents the seconds amount. 4. Write as DMS notation: 28° 14'50''

Convert DMS to DD or vice versa: DMS DD DD DMS 1. 45° 38'20'' 11. 27.4395° 2. 12° 15'45'' 12. 308.5749° 3. 50° 18'45'' 13. 45.5125° 4. 110° 19'29'' 14. 4.1031° 5. 208° 30'11'' 15. 19.9167° 6. 305° 14'33'' 16. 30.7500° 7. 78° 25'8'' 17. 68.6206° 8. 84° 55'13'' 18. 113.6550° 9. 38° 50'18'' 19. 228.4954° 10. 104° 49'9'' 20. 84.2915°

Convert from degrees to radians or vice versa: Degrees Radians Radians Degrees 21. 40° 27. p 3 22 100° 28. 3p 5 23. -225° 29. -3p 4 24 350° 30. 11p 6 25. -315° 31. -7p 3 Precalculus Name: ______Date: ______Pd: _____ 4.1 Partial Review 26. 480° 32. 9p 4 Application Problems:

1. Nancy is walking around a circular walking path. If the radius of the path is 0.50 miles and she has walked through an angle of 120 , how far has she walked?

2. Ben rides 55 feet on a merry-go-round that is 10 feet in diameter in a clockwise direction. Through what angle has Ben rotated? Round your answer to the nearest degree.

3. Approximate the area of a single slice of pizza if the entire pizza has a 14-inch diameter and the pizza is cut into 8 equal slices. Round to the nearest square inch.

4. If a sprinkler head rotates 90 and has enough pressure to keep a constant 25-foot spray, what is the area of the sector of the lawn that gets watered? Round to the nearest square foot.

5. An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its linear speed? What is its angular speed?

6. Calculate the angular velocity in radians per minute of a Ferris wheel 250 feet in diameter that takes 45 seconds to rotate once.

7. A car is moving at a rate of 65 mph, and the diameter of its wheels is 2.5 feet. What is the angular speed of the wheels in radians per minute? What is the number of revolutions per minute that the wheels are rotating? Precalculus Name: ______Date: ______Pd: _____ 4.1 Partial Review 8. A child is spinning a rock at the end of a 2-foot rope at the rate of 180 revolutions per minute. What is the linear speed of the rock when it is released?