Full resolution (JPEG) - On this page / på denna sida - Geometry - Logarithms corresponding to the trigonometrical functions - To find logarithm for secants and cosecants
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trigonometry. t 6 7
Example 3.
Find log. to tangent of 50° 45’
Solution
:
Log. tangent 50° 50’ = 0.089049
Log. tangent 50° 40’ = 0.086471
Difference 0° 10’ = 0.002578 in the logarithm. There-
fore a difference of 5’ in the angle will give 0.001289 in the
logarithm.
Thus:
Log. tangent 50° 40’ = 0.086471
Difference 5’ = 0.001289
Log. tangent 50° 45’ = 0.087760
Example 4.
Find the angle corresponding to log. tangent 9.899049 — 10.
Solution
:
Log. tangent 38° 30’ = 9.900605 — 10
Log. tangent 38° 20’ = 9.898010 — 10
Difference 0° 10’ corresponds to 0.002595
The given logarithm = 9.899049 — 10
Nearest less logarithm = 9.898010 — 10 gives 38° 20’
Difference = 0.001039
The difference to be added to the angle already found will
M01QMXW _
De 0.002595 — U 4 .
The tabulated logarithm 9.898010 — 10 gives angle 38° 20’
Difference 0.001039 gives angle 4’
Logarithm 9.899049 — 10 gives single 3S° 24’
To Find Logarithm for Secants and Cosecants.
Logarithm for secants is found by subtracting log. cosine
from log. 1.
For instance, find logarithmic secant 30°.
Solution
:
Log. 1 = 10.000000 — 10
Log. cosine 30° = 9.937531 — 10
Log. secant 30° = 0.062469
Logarithm for cosecants is found by subtracting log. sine
from log. 1. For instance, find logarithmic cosecant 35°.
Solution
:
Log. 1 -=10.000000 — 10
Log. sine 35° = 9.758591 — 10
Log. co-secant 35° = 0.241409
Note.—What is said concerning interpolations of trigono-
metrical functions in general in the note headed "Important"
on page 157, will also apply to their logarithms.
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