Plane trigonometry, by S.L. Loney.

SIN a AND COS a EXPANDED IN A SERIES.

331

sin 0
sidered. For, unless this be the case, the limit of, is
not unity when 0 is made indefinitely small.
When the angle is expressed in degrees we proceed as
follows.
Let a~= x radians, so that
a x
180 r'
and hence x = j — a.
Then cos a~ = cos x
X2 X4 X6: I - 2 + - 6 +'..
1 7r2a2 1 7r42a4 1 76a6
12180 1 804 6 1806
So also
x3 x5
sin a0 = sin x0 = x - +
7ra 1 7ra 1 t7ra
~180 o 1801 5 \18oJ 0 *.
283. Sines and cosines of small angles. The
series of Arts. 279 and 280 may be used to find the sines
and cosines of small angles.
For example, let us find the values of sin 10" and
cos 10".
Since 10" = (6 X xi ) radians
(64800) '