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The secants or cosecants are not in the tables, but may be readily found.
To find the secant, subtract the cosine from 20, and the remainder is the secant.
To find the cosecant, subtract the sine from 20, and the remainder is the cosecant.
To find the logarithmic sine, cosine, &c. of an arc to seconds.
Find the log. corresponding to the degrees and minutes, as before. Take the difference between this log. and the next greater or next less in the same column, according as you want a sine or cosine, tangent or cotangent, &c., multiply this difference by the number of seconds given, and divide the product by 60; add the quotient to the given log. if it be a sine, tangent, or secant; but subtract the quotient from the given log. if it be a cosine, cotangent, or cosecant; and the sum or remainder will be the log. required.
In a similar manner may the natural cosines, &c. be found.
To find the degrees and minutes, or degrees, minutes, and seconds corresponding to any given logarithm. Look out for the nearest logarithm to the given one, and the degrees answering to it will be found at the top, if the name be there, and the minutes in the left-hand column; but if the name be at the bottom of the table, the degrees must be found there, and the minutes in the right-hand column.
To find the arc to seconds.
Take the difference between the two nearest logs. to the given one, which you can find in the tables; also the difference between the given log. and the next less. Multiply the second difference by 60, and divide the product by the first difference; the quotient will give the seconds, which must be added to the degrees
and minutes corresponding to the nearest less number in the tables, if the given log. be a sine, tangent, or secant; but if the given logarithm be a cosine, cotan., or co-sec., the number of seconds must be deducted from the degrees and minutes corresponding to the nearest less number in the tables.
Required the degrees, minutes, and seconds corresponding to the logarithmic sine 9.43299.
Nearest sine less than the given one=9.43278
Therefore the required arc is 15° 43′ 28′′.
In the same manner may the tangent, secant, or natural sine, &c. be found.
Required the degrees, minutes, and seconds corresponding to the logarithmic cosine 9.43297.
Nearest cosine less than the given one 9.43278
Nearest cosine greater
First diff. = 45