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TRIGONOMETRY. 1 5 7
The Trigonometrical Table and Its Use.
Table No. 21 gives sine, cosine, tangent, and cotang, to
angles from to 90 degrees with intervals of 10 minutes.
For sine or tangent find the degree in the left-hand column
and find the minutes on the top of the table. For instance,
sine to 18° 40’ = 0.32006.
If cosine or cotangent is wanted, find the degree in the
column at the extreme right and the minutes at the bottom of
the table. For instance, cotang 48° 10 f
= 0.89515.
As the table only gives the angles and their trigonometrical
functions with 10-minute intervals, any intermediate angle must
be calculated by interpolations. For instance, find sine of 60°
15’ 10".
Solution:
Sine 60° 20’ 0" = 0.86892
Sine 60° 10’ 0" = 0.86748
Difference of 0° 10’ 0" = 0.00144
60° 15’ 10" — 60° 10’ 0" = 0° 5’ 10’ = 310 seconds and a
difference of 10’ = 600" increases this sine 0.00144. Therefore
a difference of 310 seconds will increase the sine.
^^=0.00074
and sine 60° 10’ 0" = 0.86748
Therefore sine 60° 15’ 5" = 0.86822
Important.—During all interpolations concerning the
trigonometrical functions, remember the fact that if the angle
is increasing both sine and tangent are also increasing, and
corrections found by interpolations must be added to the num-
ber already found ; but as the cosine and cotangent decrease
when the angle is increased, for these functions the corrections
must be subtracted.
Interpolations of this kind are not strictly correct, as neither
the trigonometrical functions nor their logarithms differ in pro-
portion to the angle. The error within such small limits as
10 minutes is very slight. When very close calculations of
great distances are required, tables are used which give the
functions with less difference than 10 minutes; but for mechan-
ical purposes in general these interpolations are correct for all
ordinary requirements. It is very seldom in a draughting office or
a machine shop that any angle is measured for a difference of
less than 10’.-
To Find Secant and Cosecant of Any Angle,
Divide 1 by cosine of the angle and the quotient is secant
of the same angle.
Divide 1 by sine of the angle and the quotient is cosecant
of the same angle.
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