Calculator method

[pabrides]

Joe,

Both of the formulas you mention in the beginning of your post are correct and yield the same result.  The Nautical Almanac specifies the second formula as entered in the Casio fx-300ES Plus calculator.  The "Sin-1" is the arc-sin key.

Anyone using the second formula should understand that by comparing it to the first formula that the first "asin" (in the first formula) and "Sin-1" in the second formula are the same thing.

To get the Hc answer correct you might do it this way;

Get the sin of Ap Lat.
Get the sin of Dec.
Multiply those two answers together and write the result down (call the product "A").

Get the cos of Ap Lat.
Get the cos of Dec.
Get the cos of LHA
Multiply those 3 answers together (call the product "B")

Add "A" and "B" together (call the sum "C")

Get the Arc-Sin of "C"
That answer will equal Hc

Craig

Thanks, I think I know trig notation well enough..  it was the sequence of operations I questioned....

So you say this is correct:

Sin-1 ((SinDec x SinLat) + (CosLat x CosDec x CosLHA))
 
This is exactly how I successfully enter it into my calculator:

Sin-1(Sin Lat x Sin Dec + Cos Lat x Cos Dec x Cos LHA)       just two brackets

To avoid confusion this might be an alternate notation (it works too when entered):

Sin-1 ((Sin Lat x Sin Dec) + (Cos Lat x Cos Dec x Cos LHA))      just 6 brackets

Original formula...   12 brackets.

 ... :)

By the way, the first two formulas provide different results - however, you may be getting the same results if you dont ask for a solution to the left side first before multiplying the last two cosines...   ((SLxSD)+CL)=A
                            AxCDxCLHA=B
Sin-1 B does not equal Sin-1 ((Sin Lat x Sin Dec) + (Cos Lat x Cos Dec x Cos LHA))

This is more fun than the law should allow.
joe

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Joe,

Take a look at these formulas- they're the same but may be of some help;

https://thenauticalalmanac.com/Formulas.html

Roland

Thanks, Roland

I must have missed that page... :)

joe