TABLE III

COMMON LOGARITHMS

OF THE

TRIGONOMETRIC FUNCTIONS

FROM

0° TO 90° AT INTERVALS OF ONE MINUTE

TO

FIVE DECIMAL PLACES .

NOTE: To find log sin a and log tan a more precisely than by ordinary interpolation, for small values of a, if a is not a tabulated angle.

Let t be the first tabulated angle below α.

Express both a and t in the

same unit (minutes, or seconds, or any other convenient unit). Then

approximately, at least to five decimal places if a <3° and a t<l'.

-

Now log α and log t can be found from Table I, and log sin t is tabulated in Table III; hence log sin a can be found. Thus to find log sin 1° 12′.4, write 1° 12′.4 = 72′.4, and arrange the computation as follows:

approximately, at least to five decimal places if a <3° and α-t<1. The method of calculation is exactly as above.

The cosines and cotangents of angles near 90° can be found by first reducing them to sines and tangents of angles near 0°. Above 3° ordinary interpolation is quite reliable, but the fifth place may be wrong in any interpolation process.

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