Plane trigonometry, by S.L. Loney.

ANGLES HAVING A GIVEN COSINE. 103
and it is therefore satisfied by
0+a 0-a
cos = 0, and by sin -2 =0,
2 2
i.e. by — + = any odd multiple of r
2 2
and by 2 = any multiple of 7r
i.e. by 0 = - a + any odd multiple of wr......(1),
and 0 = a + any even multiple of 'r......(2),
i.e. 0 must =(- 1)n a + nr, where n is any positive or
negative integer.
For when n is odd this expression agrees with (1), and
when n is even it agrees with (2).
103. Find the general value of all angles having the
same cosine.
The equation we have now to solve is
cos 0 = cos a,
i.e. cos a - cos 0 = 0,
a. a -a
i.e. 2 sin 2 sin = 0,
2 2
and it is therefore satisfied by
* O+a n - a
sin = 0, and by sin -2-a =0,
i.e. by ~ 2a = any multiple of xr,
and by any multipe
~and by -2 = any multiple of 7r,
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