Greg, Many math books and handbooks have tables of tangents; many pocket calculators will calculate them, and computer spreadsheet programs usually can calculate them also. The cotangent is the reciprocal of (that is, one divided by) the tangent. Also, the cotangent of an angle equals the tangent of 90 degrees minus the angle. See the example below. While it is possible to calculate a tangent from a formula, it is easier to get it by one of the methods above.
The tangent of 0 degrees is 0; the tangent of 90 degrees is infinite, and the tangent of 45 degrees is 1.00. These are sometimes handy values to know. Some of these calculators or spreadsheets use angles in radians rather than degrees. Experimenting with the example below will show if they do. If necessary to convert an angle to radians: multiply by pi (3.14159) and then divide by 180. Also, some methods start with degrees and fractions, others use degrees, minutes and seconds. As an example, using your 11.9 degree value: the tangent of 11.9 is 0.2107 1 / 0.2107 = 4.7453 2 inches * 4.7453 = 9.4906 inches Alternately, 2 inches / 0.2107 = 9.4906 inches Or: 90 - 11.9 = 78.1 tangent of 78.1 degrees = 4.7453 Good luck with your sundial. Gordon At 09:18 AM 7/5/98 -0700, you wrote: >I am building a sundial based on an example in Albert Waugh's book >Sunidals Their Theory and Construction, p. 137. My problem is in >computing lines of declination, however. I live in Washingotn DC at >approx. 39d West Lat. 77d N Long. I'd like to trace the sun's path for >one particular day, July 4, 1998. I believe the declination for that >day is very close to +22d.54.34.9 and the sun's altitude in degrees for >various times are as follows: >4:00 -8.5 This will not cast a shadow. The sun is below the horizon. >5:00 1.6 Shadow is 71.6 inches long; impractical to use. >6:00 11.9 >7:00 23.1 >8:00 34.6 >9:00 46.3 >10:00 57.6 >11:00 67.7 >12:00 73.7 >13:00 71.0 >14:00 62.1 >15:00 51.1 >16:00 39.5 >17:00 27.9 >18:00 16.5 >19:00 5.7 >20:00 -4.6 This will not cast a shadow. >The book states that all I must do is take the cotangent of these >altitude numbers and multiply by the height of my perpendicular style >(which is 2 inches) then measure out to the appropriate hour line. My >problem is that I cannot figure out what a cotangent is or how to >calculate one. Please help and send a detailed formula with examples so >I can compute the cotangent for other numbers. Thanks a lot in advance. > >-- > >Fiddler's Green >We Design and Install Renewable Energy Systems >"Solar Energy...Live the Good Life!" >Greg Milsom, Owner >PO Box 1200 >Bowie, Maryland 20718 >Phone/Fax: (301) 210-7669 >http://www.radix.net/~green >
