Plane trigonometry, by S.L. Loney.

A
RATIOS OF - IN TERMS OF COS A. 113
2
111. In each of the preceding formulae it will be
noted that there is an ambiguous sign. In any particular
case the proper sign can be determined as the following
examples will shew.
Ex. 1. Given cos 450= 1, find the values of sin 221~ and cos 22~0.
The equation (1) of the last article gives, by putting A equal to 45~,
sin 221= 1-cos 45 = - =
4-1 P/2- f2.
2
Now sin 22~~ is necessarily positive, so that the upper sign must be
taken.
Hence sin 221~ = 2 - 2.
So cos 22= - / os 45 2;
2 2 4
also cos 22~~ is positive;. cos 22-0 2 +s2,o5
Ex. 2. Given cos 330~=2, find the values of sin 165~ and cos 165~.
2
The equation (1) gives
sin 1650 = - cos 330~ _ _
d3-1
-2^2 '
Also
cos 165o= /1+cos 3300 = =_
2 2 8
~43 -t
2,,/2

L. T.

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