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TRIGONOMETRY. 153
TRIGONOMETRY.
Trigonometry is that branch of geometry which treats of
the solution of triangles by means of the trigonometrical
functions.
When the circumference of a circle is divided into 360 equal
parts each part is called one degree.
One fourth of a circle is 90 degrees = right angle, because
4X90 = 360. ( See Fig. 13.)
k h
"^Nmi
Im A\
’j
\
C d
Fig. 14
Circle = 4 right angles. 1 degree = 60 minutes (60’.)
Circle = 360 degrees (360°.) 1 minute = 60 seconds (60".)
Concerning the angle n (see Fig. 14) the following are the
trigonometrical functions
:
c h cosecant (cosec.)
gf tangent ( tan.)
k h cotangent (cot.)
c g radius = 1.
d b sine ( sin.)
c d cosine (cos.)
c f secant (sec.)
The complement of an angle is what remains after sub-
tracting the angle from 90°. Thus, the complement of an angle
of 30° is 60° because 90 — 30 = 60.
The sufipleinent of an angle is what remains after subtract-
ing the angle from 180°. Thus, the supplement of an angle of
30° is 150° because 180 — 30 = 150.
As all circles, regardless of their size, are divided into 360
degrees, the trigonomical functions must always be alike if the
radius and the angle that they denote are alike.
It is on this basis that the tables of trigonometrical func-
tions are calculated, and as radius is used the figure 1
.
In Table No. 21, the natural sine of 30° is given as 0.5 ; this
means that if the line c g (see Fig. 14) is 1 foot, meter, or any
other unit, and the angle n is 30 degrees, the line d b will be 0.5
of the same unit as the line eg.
Sine 45° == 0.70711 ; that is, if the the angle n is 45 degrees
and the line c g is 1 of any unit, the line d b is 0.70711 of the
same unit.
Cos. 30° = 0.86603 ; that is, if the angle «.is 30 degrees and
the line c g is 1 of any unit, the line a b or c d is 0.86603 of the
same unit.
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