Six Place Logarithmic Tables: Together with a Table of Natural Sines, Cosines, Tangents, and Cotangents1891 - Logarithms - 79 pages |
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Page vii - Note IX. In searching for the next less (or greater) logarithm, attention must be paid to the fact that the functions are found in different columns according as the angle is below or above 45°. If, for example, the next less logarithmic sine is found in the column with
Page x - This is correct to the sixth place of decimals ; the result by the table of logarithmic tangents is 8.103375 — 10. To find the angle corresponding to a given logarithmic sine or tangent, when between 0° and 5°. Find from the table of logarithmic functions the angle corresponding to the given logarithm, to the nearest second. Take from the auxiliary table the logarithm corresponding to this angle. Subtract the result from the given logarithm, and find the number corresponding to the difference,...
Page vi - For angles between 0° and 45°, the degrees will be found at the top of the page, the minutes in the left.hand column, and the functions in the columns designated by the names at the top; that is, sines in the first column, cosines in the second, tangents in the third, and cotangents in the fourth. For angles between 45° and 90°, the degrees will be...
Page xi - ... and 90°, find the logarithmic cotangent of the angle as above, and subtract the result from 10 — 10. (Note XI.) To find the angle corresponding to a logarithmic tangent in the same case, find the logarithmic cotangent of the angle (Note XL), and find the angle corresponding to the result. These methods also serve to determine the logarithmic cotangent of an angle between 0° and 5°, or the angle corresponding in the same case. A TABLE CONTAINING THE LOGARITHMS OF NUMBERS FROM 1 TO 10,000.
Page x - XIII. To find a natural function to a greater degree of accuracy than is possible from the table of natural functions, we may find the logarithmIc function of the angle, and take the number corresponding to the result. IV. USE OF THE AUXILIARY TABLE FOR SMALL ANGLES. This table (page 79) gives the values of the expressions 10 + log sin x — log x and 10 + log tan x — log x, x being expressed in seconds, for all angles at intervals of 1' from 0° to 4° 59'. It may be used to find the logarithmic...
Page iii - Required the logarithm of 3296.78. We find from the table, log 3296 = 3.517987 ; log 3297 = 3.518119. That is, an increase of one unit in the number produces an increase of .000132 in the logarithm. Then an increase of .78 of a unit in the number will produce an increase of .78 x .000132 in the logarithm...
Page ix - Its use is similar to that of the table of logarithmic functions, except that the tabular differences for 1" are not given, but are to be calculated from the table when required. 1. Required tan 41° 27' 14". tan 41° 27' = .88317. The difference between this and tan 41° 28' is 52. Correction for 14" = ~ x 52 = 12, nearly. DU .88317 12 Result, .88329 2. Required the angle whose cos = .45854. Next greater cos = .45865 ; angle corresponding = 62° 42'.
Page viii - ... right.hand column. Similar considerations hold with respect to the other three functions. 1. Find the angle whose log sin = 9.959345 — 10. 9.959345 - 10 Next less log sin = 9.959310 — 10 ; angle corresponding = 65° 35'.
Page 32 - ... 19 18 17 16 15 14 13 12 II IO 9 8 7 6 5 4 3 2 I O Cos. D. 1". Sin. D. 1". Cot. D. 1". Tan. M. LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS. 19° 87 70° и. Sin. D. 1". Cos. D. 1". Tan. D. 1".
Page vi - ... 10. To find the logarithmic sine, cosine, tangent, or cotangent of any acute angle expressed in degrees, minutes, and seconds. Find from the table the logarithmic sine, cosine, tangent, or cotangent of the degrees and minutes, and the difference for 1