Plane trigonometry, by S.L. Loney.

ANGLES OF 9~ AND 81~.

129

123. To find the trigonometrical functions for an angle
of 9~.
Since sin 9~ and cos 90 are both positive the relation
(3) of Art. 113 gives
sin 9~ + cos 9~ = /1 + sin 18~= /1 + 1 5- - 13+/5
V 4 2...............(1).
Also, since cos 9~ is greater than sin 9~ (Art. 53), the
quantity sin 9~ - cos 9~ is negative. Hence the relation
(4) of Art. 113 gives
sin 9 - cos 9~= - sin 8~= - V/I - V5- 1
_ /5- /5 -2(2).
2...............(2).
By adding (1) and (2), we have
sin 9 3 + /5 - /5 - 1/5
sin 90 =
4
and, by subtracting (2) from (1), we have
cos 9~ _- 3 + s/5 + /5 - /5
4
The remaining functions for 9~ may now be found.
Also, since 81~ is the complement of 9~, the values of
the functions for 81~ may be obtained by the use of
Art. 69.
EXAMPLES. XIX.
Prove that
1. sin2 720- sin2600=/5 -2. cos2 48~ - sin2 120 =^5 + 1
L

L. T.

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