39° 20′ 3′ 54′′ cosine is .7742.

39° 16' 6", which is the angle whose

Looking down the eighth column, headed cos, the next smaller cosine is .7735, to which corresponds the angle 39° 20'. The difference for 10' is 18. Subtracting, the remainder is 7, and the next lower number in the table of proportional parts is 5.4, which is the difference for 3'. Subtracting this from 1st remainder, 2d remainder is 1.6, which is nearest 16.2 of table of proportional parts, if the decimal point of the latter is moved to the left one place. Since 16.2 corresponds to a difference of 9', 1.62 corresponds to a difference of .9', or 54". Hence, the correction for the angle 39° 20' is 3′ 54′′. From the table, it appears that, as the cosine increases, the angle grows smaller; therefore, the angle whose cosine is .7742 must be smaller than the angle whose cosine is .7735, and the correction for the angle must be subtracted. Find the angle whose cotangent is .9847.

45° 30'-3' 30" = 45° 26' 30', the angle whose cotangent is .9847.

In finding the angle corresponding to a function, as in the above examples, the angles obtained may vary from the true angle by 2 or 3 seconds; in order to obtain the number of seconds accurately, the functions should contain six or seven decimal places.