Plane trigonometry, by S.L. Loney.

RATIOS OF A IN TERMS OF SIN A. 117
Hence the above two relations should be
sin 15~ + cos 15~ = +12'
and sin 15~ - cos 15~=,.
Hence sin 15~ =/2 and cos 15 =o3+1
2 ad 2/2 cos 15= 1
Ex. 2. Given that sin 570~ is equal to - 2,find the values of sin 285~
and cos 285~.
Putting A equal to 570~, we have
sin 285~ + cos 285~ =: ^/1 + sin 570~ = A /and sin 285~ - cos 285~ = A ^1 - sin 570~ = /.
Now sin 285~ is negative, cos 285~ is positive, and the former is
numerically greater than the latter, as may be seen by a figure.
Hence sin 285~ + cos 285~ is negative and sin 285~- cos 285~ is also
negative... sin 285~ + cos 285~= -
dV2'
and sin 285~ - cos 285~ = - /3.
Hence sin 285~ = - +1
212
and cos 285~ =3-1
A
##115. To explain why there is ambiguity when sin A
2
A
and cos - are found from the value of sin A.
2
We know that, if ni be any integer,
sin {nr + (- 1)n A} = sin A = k (say). (Art. 82.)