- #1
moja_a
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Homework Statement
if:
H = Local Hour Angle
Lat = Latitude.
Dec = Sun Declination.
cos(H) = -sin(a)-sin(Lat)*sin(Dec) / cos(Lat)*cos(Dec)
I wand to get The value of Lat .
The Attempt at a Solution
I Tried to make it simple By :
1 - multiply both sides by the denominator
1- square both sides
2- Rewrite cos^2(L) as 1-sin^2(L)
3- Rearrange into a quadratic equation in sin(L).
And this is what I got:
Cos^2(H).Cos^2(D).Cos^2(L) = -Sin^2(a) - 2Sin(a).Sin(D).Sin(L) + Sin^2(L).Sin^2(D)
Cos^2(H).Cos^2(D).(1-Sin^2(L) )= -Sin^2(a) - 2Sin(a).Sin(D).Sin(L) + Sin^2(L).Sin^2(D)
Cos^2(H).Cos^2(D) - Cos^2(H).Cos^2(D).Sin^2(L) = - Sin^2(a) - 2Sin(a).Sin(D).Sin(L) + Sin^2(L).Sin^2(D)
Cos^2(H).Cos^2(D) = -Sin^2(a)- 2Sin(a).Sin(D).Sin(L) + Sin^2(L).Sin^2(D) + Cos^2(H).Cos^2(D).Sin^2(L)
Cos^2(H).Cos^2(D) = -Sin^2(a)- 2Sin(a).Sin(D).Sin(L) + Sin^2(L) . ( Sin^2(D) + Cos^2(H).Cos^2(D) )
then I am Stuck can you help me please.