Plane trigonometry, by S.L. Loney.

GRAPHIC SOLUTION.

141

Next find from the tables, or otherwise, the angle a
whose cosine is
2/a2+b2
so that cos B= c
/a2+ b2
[N.B. This can only be done when c is < Va2 + b2.]
The equation is then cos (0 - a) = cos,.
The solution of this is 0 - a = 2n7r + F3, so that
0= 2n7r+ a + 3,
where n is any integer.
Angles, such as a and /, which are introduced into
trigonometrical work to facilitate computation are called
Subsidiary Angles.
130. The above solution may be illustrated graphically
as follows;
Measure OM along the initial \
Q
line equal to a, and MP perpendicular to it, and equal to b. The A
angle MOP is then the angle whose \ OM N
tangent is -, i.e. a. \
With centre 0 and radius OP,
i.e. Va2/~+b2, describe a circle and measure ON~ along
the initial line equal to c.
Draw QNQ' perpendicular to ON to meet the circle in
Q and Q'; the angles NOQ and Q'ON are therefore each
equal to 13.
The angle QOP is therefore a -/, and Q'OP is a + 3.