Machinery's Handbook, 31st Edition
ANGLE CONVERSIONS 103 Conversion Tables of Angular Measure.— The accompanying tables of degrees, min utes, and seconds into radians; radians into degrees, minutes, and seconds; radians into degrees and decimals of a degree; and minutes and seconds into decimals of a degree and vice versa facilitate the conversion of measurements. Example 1: The “Degrees, Minutes, and Seconds into Radians” table is used to find the number of radians in 324 degrees, 25 minutes, 13 seconds as follows: 300 degrees = 5.235988 radians 20 degrees = 0.349066 radian 4 degrees = 0.069813 radian 25 minutes = 0.007272 radian 13 seconds = 0.000063 radian 324 ° 25 ′ 13 ″ = 5.662202 radians Example 2: The “Radians into Degrees and Decimals of a Degree,” and “Radians into Degrees, Minutes and Seconds” tables are used to find the number of decimal degrees or degrees, minutes and seconds in 0.734 radian as follows: 0.7 radian = 40.1070 degrees 0.7 radian = 40 ° 6 ′ 25 ″ 0.03 radian = 1.7189 degrees 0.03 radian = 1 ° 43 ′ 8 ″ 0.004 radian = 0.2292 degree 0.004 radian = 0°13 ′ 45 ″ 0.734 radian = 42.0551 degrees 0.734 radian = 41 ° 62 ′ 78 ″ or 42 ° 3 ′ 18 ″ Degrees, Minutes, and Seconds into Radians (Based on 180 degrees = π radians) Degrees into Radians Deg. Rad. Deg. Rad. Deg. Rad. Deg. Rad. Deg. Rad. Deg. Rad. 1000 17.453293 100 1.745329 10 0.174533 1 0.017453 0.1 0.001745 0.01 0.000175 2000 34.906585 200 3.490659 20 0.349066 2 0.034907 0.2 0.003491 0.02 0.000349 3000 52.359878 300 5.235988 30 0.523599 3 0.052360 0.3 0.005236 0.03 0.000524 4000 69.813170 400 6.981317 40 0.698132 4 0.069813 0.4 0.006981 0.04 0.000698 5000 87.266463 500 8.726646 50 0.872665 5 0.087266 0.5 0.008727 0.05 0.000873 6000 104.719755 600 10.471976 60 1.047198 6 0.104720 0.6 0.010472 0.06 0.001047 7000 122.173048 700 12.217305 70 1.221730 7 0.122173 0.7 0.012217 0.07 0.001222 8000 139.626340 800 13.962634 80 1.396263 8 0.139626 0.8 0.013963 0.08 0.001396 9000 157.079633 900 15.707963 90 1.570796 9 0.157080 0.9 0.015708 0.09 0.001571 10000 174.532925 1000 17.453293 100 1.745329 10 0.174533 1.0 0.017453 0.10 0.001745 Minutes into Radians Min. Rad. Min. Rad. Min. Rad. Min. Rad. Min. Rad. Min. Rad. 1 0.000291 11 0.003200 21 0.006109 31 0.009018 41 0.011926 51 0.014835 2 0.000582 12 0.003491 22 0.006400 32 0.009308 42 0.012217 52 0.015126 3 0.000873 13 0.003782 23 0.006690 33 0.009599 43 0.012508 53 0.015417 4 0.001164 14 0.004072 24 0.006981 34 0.009890 44 0.012799 54 0.015708 5 0.001454 15 0.004363 25 0.007272 35 0.010181 45 0.013090 55 0.015999 6 0.001745 16 0.004654 26 0.007563 36 0.010472 46 0.013381 56 0.016290 7 0.002036 17 0.004945 27 0.007854 37 0.010763 47 0.013672 57 0.016581 8 0.002327 18 0.005236 28 0.008145 38 0.011054 48 0.013963 58 0.016872 9 0.002618 19 0.005527 29 0.008436 39 0.011345 49 0.014254 59 0.017162 10 0.002909 20 0.005818 30 0.008727 40 0.011636 50 0.014544 60 0.017453 Seconds into Radians Sec. Rad. Sec. Rad. Sec. Rad. Sec. Rad. Sec. Rad. Sec. Rad. 1 0.000005 11 0.000053 21 0.000102 31 0.000150 41 0.000199 51 0.000247 2 0.000010 12 0.000058 22 0.000107 32 0.000155 42 0.000204 52 0.000252 3 0.000015 13 0.000063 23 0.000112 33 0.000160 43 0.000208 53 0.000257 4 0.000019 14 0.000068 24 0.000116 34 0.000165 44 0.000213 54 0.000262 5 0.000024 15 0.000073 25 0.000121 35 0.000170 45 0.000218 55 0.000267 6 0.000029 16 0.000078 26 0.000126 36 0.000175 46 0.000223 56 0.000271 7 0.000034 17 0.000082 27 0.000131 37 0.000179 47 0.000228 57 0.000276 8 0.000039 18 0.000087 28 0.000136 38 0.000184 48 0.000233 58 0.000281 9 0.000044 19 0.000092 29 0.000141 39 0.000189 49 0.000238 59 0.000286 10 0.000048 20 0.000097 30 0.000145 40 0.000194 50 0.000242 60 0.000291
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