Plane trigonometry, by S.L. Loney.

264

TRIGONOMETRY.

we have sin 10' sin (180x6 - 180
3.14159265...
31415 = 0029089 nearly.
180 x 6
Also cos 10' = /1 - sin2 10'
=[1 - 000008468...]3
=1 - [000008468...],
approximately by the Binomial Theorem,
=1- 000004234...
= 9999958....
Ex. 2. Solve approximately the equation
sin 0 = 52.
1
Since sin 8 is very nearly equal to - 0 must be nearly equal to
' 6'
Let then 0 = +x, where x is small..'.'52 =sin + )=~~ n.. 52= sin (7 + = sin cos x + cos sin x
6 6 6
1 3.:2 cos x + - sin x.
J2 2
Since x is very small, we have
cos x= 1 and sin x = x nearly..52=I +- x.
2 2
X. x =02 x 3 radians = 3= 1320 nearly.
-J3 75
Hence 0= 31~ 19' nearly.
EXAMPLES. XL.
Taking r equal to 3-14159265, find to 5 places of decimals the
value of
1. sin 7'. 2. sin 15". 3. sin 1'.
4, cos 15'. 5. cosec 8". 6. sec 5'.