[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
