Plane trigonometry, by S.L. Loney.

140 TRIGONOMETRY.
By the formulae of Art. 94 the equation is
2 sin 3x cos 2x = sin 3x... sin 3x = 0, or 2 cos 2x = 1.
If sin 3x = 0, then 3x = nwr.
I 7r
If cos 2x = then 2x = 27r +.
2t o
nrT 7r
Hence =, or n7r +
o 6
129. To solve an equation of the forn
a cos 0 + b sin 0 = c.
Divide both sides of the equation by V/a + b2, so that
it may be written
a cos b c
- cos0 __ sin 0=
Va2 +2 a2 + b2 a2 + b2
Find from the table of tangents the angle whose
tangent is b and call it a.
b
Then tan a =-, so that
a
b a
sin a =, and cos a -
2a b2 2a2b'
The equation can then be written
cos a cos 0 + sin a sin 0= A- '
i.e. cos (0 - a)= _.
/a2o+b2