Plane trigonometry, by S.L. Loney.

58

TRIGONOMETRY.

Similarly as the angle increases from 27r radians to
47r radians, the sine goes through the same series of
changes.
Also the sines of any two angles which differ by four
right angles, i.e. 27r radians, are the same.
This is expressed by saying that the period of the
sine is 27r.
Similarly the cosine, secant, and cosecant go through
all their changes as the angle increases by 2vr.
The tangent, however, goes through all its changes as
the angle increases from 0 to 7r radians, i.e. whilst the
revolving line turns through two right angles. Similarly
for the cotangent.
The period of the sine, cosine, secant and cosecant is
therefore 27r radians; the period of the tangent and
cotangent is vr radians.
Since the values of the trigonometrical functions
repeat over and over again as the angle increases, they
are called periodic functions.
#62. The variations in the values of the trigonometrical ratios may be graphically represented to the eye
by means of curves constructed in the following manner.
R1I', \d- R\3 R4 "'
"": -,
R~".. ',/ P R1 'v R5 X
~Bie~' e ~B
Sine-Curve.
Let OX and OY be two straight lines at right angles