Plane trigonometry, by S.L. Loney.

334

TRIGONOMETRY.

so that
2 1 2V/3 3-4641...
3 3- 0 30l0 = -011547... radian.
For a still nearer approximation, omit cubes and higher powers of 0.
The equation (1) then becomes
1 02 ) /3 1 =
2 2 2 100'
i.e. 02+2V/30 =o.
100'.. 0= -^3+ /304 = ='0115086... radian.
The first approximation is therefore correct to 4 places of decimals.
The angle 0 is therefore very nearly equal to '0115 radian, i.e. to
about 40'.
The accurate answer is found, from the tables, to be *0115075...
radian.
285. Evaluation of quantities apparently indeterminate. We often have to obtain the value of quantities which are apparently indeterminate.
Suppose we required the value of the expression
3 sin 0 -sin 30
0 (cos 0 - cos 30)'
when 0 is zero.
If we substitute the value 0 for 0, we have
0 x 0'
which is apparently indeterminate.
The expression however, for all values of 0,
3 sin -(3 sin - 4sin38) 4 sin38
{o0 {scos- cos3 0- 3 cos 0)} ~ {4 cos 0 -4 cos 0}
sin 0 sin 0 1 sin 0
0 cos 0 sin 0 0 cos0 = cos 0 0