I need help with questions 1-15

6.1 Angle Measure 367 When applying these results 0 is in radians, the same linear units are used for r and s, and the same units of time are used for v and w. if the EXAMPLE 5 Assuming the earth's radius to be 4000 miles, find the linear speed of a point on the equator in mph and also in ft/sec. What is the angular speed in radians per hour (rad/hr)? Equator how in 3 4000 mi. 120 evel Solution As the earth makes one complete rotation in 24 hours, the angular rotation ori- is 2 17 radians. Thus 1 re- distance arc ro (4000) (2TT) ard -= 1047 24 USLD DUUR ear The linear speed is 1047 mph rounded to the nearest mph. Since 1 mile = 5280 feet and 1 hour = (60) (60) = 3600 seconds. v = 1047 mph = 1047(5280) ft/hr 1047(5280) ft/sec 3600 = 1536 ft/sec on re volute nearest foot per second Note Also, the angular speed w is given by rad/hr = 7 180 12 T w - @ 2 TT TT rad/ hr = 150 per hour. t 24 12 ar lar EXERCISES 6.1 Convert the degrees to radians. Leave the answers in terms of T. e 1, 450 5. 270 2. 60 3. 90 4. 180 6. 360 9. 2250 10. 240 7. 150 8. 1350 11. 2100 15. 750 12. 300 13. 330 14. 3450