Degrees

Part θ θ ÷ 2 π Radians sin θ cos θ tan θ
0.0000 0.0° 0.00° 0/2 0/3 0/4 0/6 0/8 0/12 +0.000000 +1.000000 +0.000000
0.0208 7.5° 3.75° +0.130526 +0.991445 +0.131652
0.0417 15.0° 7.50° 1/12 +0.258819 +0.965926 +0.267949
0.0625 22.5° 11.25° 1/8 +0.382683 +0.923880 +0.414214
0.0833 30.0° 15.00° 1/6 2/12 +0.500000 +0.866025 +0.577350
0.1042 37.5° 18.75° +0.608761 +0.793353 +0.767327
0.1250 45.0° 22.50° 1/4 2/8 3/12 +0.707107 +0.707107 +1.000000
0.1458 52.5° 26.25° +0.793353 +0.608761 +1.303225
0.1667 60.0° 30.00° 1/3 2/6 4/12 +0.866025 +0.500000 +1.732051
0.1875 67.5° 33.75° 3/8 +0.923880 +0.382683 +2.414214
0.2083 75.0° 37.50° 5/12 +0.965926 +0.258819 +3.732051
0.2292 82.5° 41.25° +0.991445 +0.130526 +7.595754
0.2500 90.0° 45.00° 1/2 2/4 3/6 4/8 6/12 +1.000000 +0.000000
0.2708 97.5° 48.75° +0.991445 -0.130526 -7.595754
0.2917 105.0° 52.50° 7/12 +0.965926 -0.258819 -3.732051
0.3125 112.5° 56.25° 5/8 +0.923880 -0.382683 -2.414214
0.3333 120.0° 60.00° 2/3 4/6 8/12 +0.866025 -0.500000 -1.732051
0.3542 127.5° 63.75° +0.793353 -0.608761 -1.303225
0.3750 135.0° 67.50° 3/4 6/8 9/12 +0.707107 -0.707107 -1.000000
0.3958 142.5° 71.25° +0.608761 -0.793353 -0.767327
0.4167 150.0° 75.00° 5/6 10/12 +0.500000 -0.866025 -0.577350
0.4375 157.5° 78.75° 7/8 +0.382683 -0.923880 -0.414214
0.4583 165.0° 82.50° 11/12 +0.258819 -0.965926 -0.267949
0.4792 172.5° 86.25° +0.130526 -0.991445 -0.131652
0.5000 180.0° 90.00° 2/2 3/3 4/4 6/6 8/8 12/12 +0.000000 -1.000000 -0.000000
0.5208 187.5° 93.75° -0.130526 -0.991445 +0.131652
0.5417 195.0° 97.50° 13/12 -0.258819 -0.965926 +0.267949
0.5625 202.5° 101.25° 9/8 -0.382683 -0.923880 +0.414214
0.5833 210.0° 105.00° 7/6 14/12 -0.500000 -0.866025 +0.577350
0.6042 217.5° 108.75° -0.608761 -0.793353 +0.767327
0.6250 225.0° 112.50° 5/4 10/8 15/12 -0.707107 -0.707107 +1.000000
0.6458 232.5° 116.25° -0.793353 -0.608761 +1.303225
0.6667 240.0° 120.00° 4/3 8/6 16/12 -0.866025 -0.500000 +1.732051
0.6875 247.5° 123.75° 11/8 -0.923880 -0.382683 +2.414214
0.7083 255.0° 127.50° 17/12 -0.965926 -0.258819 +3.732051
0.7292 262.5° 131.25° -0.991445 -0.130526 +7.595754
0.7500 270.0° 135.00° 3/2 6/4 9/6 12/8 18/12 -1.000000 -0.000000
0.7708 277.5° 138.75° -0.991445 +0.130526 -7.595754
0.7917 285.0° 142.50° 19/12 -0.965926 +0.258819 -3.732051
0.8125 292.5° 146.25° 13/8 -0.923880 +0.382683 -2.414214
0.8333 300.0° 150.00° 5/3 10/6 20/12 -0.866025 +0.500000 -1.732051
0.8542 307.5° 153.75° -0.793353 +0.608761 -1.303225
0.8750 315.0° 157.50° 7/4 14/8 21/12 -0.707107 +0.707107 -1.000000
0.8958 322.5° 161.25° -0.608761 +0.793353 -0.767327
0.9167 330.0° 165.00° 11/6 22/12 -0.500000 +0.866025 -0.577350
0.9375 337.5° 168.75° 15/8 -0.382683 +0.923880 -0.414214
0.9583 345.0° 172.50° 23/12 -0.258819 +0.965926 -0.267949
0.9792 352.5° 176.25° -0.130526 +0.991445 -0.131652
1.0000 360.0° 180.00° 4/2 6/3 8/4 12/6 16/8 24/12 -0.000000 +1.000000 -0.000000
2.0000 720.0° 360.00° 8/2 12/3 16/4 24/6 32/8 48/12 +0.000000 +1.000000 0.0
3.0000 1080.0° 540.00° 12/2 18/3 24/4 36/6 48/8 72/12 +0.000000 +1.000000 0.0
4.0000 1440.0° 720.00° 16/2 24/3 32/4 48/6 64/8 96/12 +0.000000 +1.000000 0.0
5.0000 1800.0° 900.00° 20/2 30/3 40/4 60/6 80/8 120/12 +0.000000 +1.000000 0.0
6.0000 2160.0° 1080.00° 24/2 36/3 48/4 72/6 96/8 144/12 +0.000000 +1.000000 0.0
7.0000 2520.0° 1260.00° 28/2 42/3 56/4 84/6 112/8 168/12 +0.000000 +1.000000 0.0
8.0000 2880.0° 1440.00° 32/2 48/3 64/4 96/6 128/8 192/12 +0.000000 +1.000000 0.0
9.0000 3240.0° 1620.00° 36/2 54/3 72/4 108/6 144/8 216/12 +0.000000 +1.000000 0.0

Unit Circle

(Under development.)

Table Generator (Python Code)

001| ####################################################################################################
002| from sys import argv
003| from os import path
004| from math import pi,tau, sin,cos,tan
005| ####################################################################################################
006| BasePath = r'C:\CJS\www\root\lib\info'
007| Segments = 48
008| 
009| table_top = '''\
009| <table class="StandardTable">
009| <thead>
009| <tr>
009|  <th>Part</th>
009|  <th>&theta;</th>
009|  <th>&theta; &div; 2</th>
009|  <th colspan="6">&pi; Radians</th>
009|  <th>sin &theta;</th>
009|  <th>cos &theta;</th>
009|  <th>tan &theta;</th>
009| </tr>
009| </thead>
009| <tbody>'''
010| 
011| table_row = '''\
011| <tr id='row%d'>
011|  <td>%.4f</td>
011|  <td>%.1f&deg;</td>
011|  <td>%.2f&deg;</td>
011|  <td>%s</td>
011|  <td>%s</td>
011|  <td>%s</td>
011|  <td>%s</td>
011|  <td>%s</td>
011|  <td>%s</td>
011|  <td>%+.6f</td>
011|  <td>%+.6f</td>
011|  <td>%s</td>
011| </tr>'''
012| 
013| table_bot = '''\
013| </tbody>
013| </table>'''
014| 
015| fn = path.join(BasePath, '_circle.html')
016| fp = open(fn, mode='w', encoding='utf8')
017| try:
018|     print(table_top, file=fp)
019|     for ix in range(Segments+1):
020|         ce = ix/Segments
021|         de = 360.0 * ce
022|         p2 = '' if ix % 12 else ('%d/2'%(ix/12))
023|         p3 = '' if ix %  8 else ('%d/3'%(ix/ 8))
024|         p4 = '' if ix %  6 else ('%d/4'%(ix/ 6))
025|         p6 = '' if ix %  4 else ('%d/6'%(ix/ 4))
026|         p8 = '' if ix %  3 else ('%d/8'%(ix/ 3))
027|         pc = '' if ix %  2 else ('%d/12'%(ix/2))
028|         si = sin(tau * ce)
029|         co = cos(tau * ce)
030|         ta = ('%+.6f'%tan(tau * ce)) if ((ix+12) % 24) else ''
031|         t = (ix, ce, de,de/2.0, p2,p3,p4,p6,p8,pc, si,co,ta)
032|         print(table_row % t, file=fp)
033| 
034|     for ix in [Segments*n for n in range(2,10)]:
035|         ce = ix/Segments
036|         de = 360.0 * ce
037|         p2 = '' if ix % 12 else ('%d/2'%(ix/12))
038|         p3 = '' if ix %  8 else ('%d/3'%(ix/ 8))
039|         p4 = '' if ix %  6 else ('%d/4'%(ix/ 6))
040|         p6 = '' if ix %  4 else ('%d/6'%(ix/ 4))
041|         p8 = '' if ix %  3 else ('%d/8'%(ix/ 3))
042|         pc = '' if ix %  2 else ('%d/12'%(ix/2))
043|         t = (ix, ce, de,de/2.0, p2,p3,p4,p6,p8,pc, 0.0,1.0,0.0)
044|         print(table_row % t, file=fp)
045| 
046|     print(file=fp)
047|     print(table_bot, file=fp)
048| except:
049|     raise
050| finally:
051|     fp.close()
052|     print('wrote: %s' % fn)
053| 
054| print()
055| ####################################################################################################
056| '''eof'''
057|