[EMAIL PROTECTED] writes: > Could someone help me solve for declination of the sun or latitude > from the equation for altitude: > > sin(Alt)=sin(dec)*sin(lat) + cos(dec)*cos(lat)*cos(local hour angle) > > I would like to know how this is solved as much as just knowing the > answer.
You want to add a sine wave and and a cosine wave with different amplitudes. The result will be a sine wave with a phase shift. Use the trig identity: sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) My "a" will be your "dec". My "b" can be found from the ratio of the coefficients: coefficient of cos(a) cos(lat)*cos(local hour angle) tan(b) = --------------------- = ------------------------------ coefficient of sin(a) sin(lat) We have to multiply both sides of your equation by 2 2 -1/2 c = [ ( sin(lat) ) + ( cos(lat)*cos(local hour angle) ) ] so that the sum of the coefficients, cos(b)^2 + sin(b)^2, is unity. Then we have: sin(a+b) = c*sin(Alt) Written out (nearly) in full: dec = -arctan( cot(lat)*cos(local hour angle) ) + arcsin( c*sin(Alt) ) [Disclaimer: Don't believe it or use it until you or someone else has checked it.] --Art Carlson-- [EMAIL PROTECTED] http://www.ipp.mpg.de/~Arthur.Carlson/home.html