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1 66 TRIGONOMETRY,
Logarithms Corresponding to the Trigonometrical
Functions.
Table No. 22 gives the logarithms corresponding to sine,
cosine, tangent and cotang. for angles from to 90 degrees,
with intervals of 10 minutes. For sine and tangent find the
degree in the column to the left and the minutes at the top of
the table. For instance
:
Log. sine 19° 30’ = 9.523495 — 10.
This, of course, is also logarithm to the fraction 0.33381,
which is sine of 19° 30’.
For cosine and cotang. find the degree in the column to the
extreme right in the table, and find the minutes at the bottom
of table. For instance
:
Log. cotang. 37° 10’ = 10.120259 — 10 = 0.120259.
Note.—In this table the index of the logarithm is increased
by 10, therefore — 10 must always be annexed in the logarithm.
Logarithms to angles between those in the table may be
obtained by interpolations. For instance, find log. sine 25° 45’.
Solution:
Log. sine 25° 50’ — 9.639242 — 10
Log. sine 25° 40’ — 9.636623 — 10
Difference 0.002619
This difference in the logarithm corresponds to a difference
in this angle of 10 minutes ;
therefore a difference of 5 minutes
in the angle will make a difference of 0.001309 in the logarithm.
Thus
:
Log. sine 25° 40’ = 9.636623 — 10
Difference 5’ — 0.001309
Log. sine 25° 45’ = 9.637932 — 10
Example 2.
Find angle corresponding to logarithmic sine 9.894246 — 10.
Solution
:
In the table of logarithms of sine :
9.894546 — 10 corresponds to 51° 40’
9.893544 — 10 corresponds to 51° 30’
Difference 0.001002 corresponds to 0° 10~’
To logarithm 9.894246 — 10 must, therefore, correspond an
angle somewhere between 51° 30’ and 51° 40’, which is found
thus:
The given logarithm is 9.894246 — 10
Nearest less logarithm 9.893544 — 10 for 51° 30’
Difference 0.000702
Therefore, the correction to be added to the angle already
found will be
:
0.0007Q2 x io
_
0.001002 ~~ u •
Thus, the logarithmic sine 9.894246 — 10 gives 51° 37’
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