Plane trigonometry, by S.L. Loney.

ANGLES OF 18~ AND 36~.

127

In our case sin 0 is necessarily a positive quantity.
Hence we take the upper sign, and have
sin 180 =- 1
4
Hence
cos 18 = V/-in2 18 = 6_- 21 _ 5v 0 + 2215
16 16
110 + 225
4
The remaining trigonometrical ratios of 18~ may be
now found.
Since 72~ is the complement of 18~, the values of the
ratios for 72~ may be obtained by the use of Art. 69.
121. To find the trigonometrical finctions of an angle
of 36.
Since cos 20 = 1 - 2 sin2 0, (Art. 105),
cos 36~=1 -2 sin2 18= 1-2 ( -6 )
3-25
1
— 14 +
so that cos 36~0= +
4
Hence
*ifl 601i CO52360,\//1 6+21/5 110-21/5
sin 36~ = Vl-cos 36~ = 1- 6 -2 4 -16 4
The remaining trigonometrical functions of 36~ may
now be found.
Also, since 54~ is the complement of 36~, the values of
the functions for 54~ may be found by the help of Art. 69.
122. The value of sin 18~ and cos 36~ may also be
found geometrically as follows.