The following paraphrased excerpt is from the 2018 Nautical Almanac:
Determine Hc using a calculator
Hc = asin[sin(Declination)*sin(Latitude) + cos(Latitude)*cos(Declination)*cos(LHA)]
As it would be entered into the Casio calculator
Sin-1(Sin(Ap Latitude) x Sin(Declination) + Cos(Ap Latitude) x Cos(Declination) x Cos(LHA)
Instantly one sees these two formulas are not the same. The second formula is missing an operation bracket and one set of operations are transposed. But that's only half the problem. It is unclear which operation comes first. Is cos lat added to sin lat before being multiplied to the first sin dec... is one question.
I think you understand the operational problems here. Some calculators dont take anything for granted, while some operate to the normal order of operations - as in multiply first then add.
Which of the following is right??? (I removed some brackets for clarity)
Hc = Sin-1 ((SinDec x SinLat) + (CosLat x CosDec x CosLHA))
or
Hc = Sin-1 (((SinDec x SinLat) + CosLat) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinDec (SinLat + CosLat)) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinLat (Sin (Dec + CosLat))) x CosDec x CosLHA)
Or something else??? My calculator shows an error using the original formula
Please be clear if you offer a formula in response.
joe
Determine Hc using a calculator
Hc = asin[sin(Declination)*sin(Latitude) + cos(Latitude)*cos(Declination)*cos(LHA)]
As it would be entered into the Casio calculator
Sin-1(Sin(Ap Latitude) x Sin(Declination) + Cos(Ap Latitude) x Cos(Declination) x Cos(LHA)
Instantly one sees these two formulas are not the same. The second formula is missing an operation bracket and one set of operations are transposed. But that's only half the problem. It is unclear which operation comes first. Is cos lat added to sin lat before being multiplied to the first sin dec... is one question.
I think you understand the operational problems here. Some calculators dont take anything for granted, while some operate to the normal order of operations - as in multiply first then add.
Which of the following is right??? (I removed some brackets for clarity)
Hc = Sin-1 ((SinDec x SinLat) + (CosLat x CosDec x CosLHA))
or
Hc = Sin-1 (((SinDec x SinLat) + CosLat) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinDec (SinLat + CosLat)) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinLat (Sin (Dec + CosLat))) x CosDec x CosLHA)
Or something else??? My calculator shows an error using the original formula
Please be clear if you offer a formula in response.
joe