Plane trigonometry, by S.L. Loney.

MAXIMUM VALUE.

145

Since the greatest value of the quantity cos (0 - a) is
unity, i.e. when 0 equals a, the greatest value of the
expression is /a2 + b2.
Also the value of 0 which gives this greatest value is
such that its cosine is +
/a2 + b2'
EXAMPLES. XXII.
As 0 increases from 0 to 360~, trace the changes in the sign and
magnitude of
1. sin 0- cos 0,
2. sin0+,/3cos 0,
[N.B. sin 0 +V3 cos 0=2 sin 0+ 32 cos 0]=2 sin ( + 60~).]
3. sin 0 - /3 cos 0. 4. cos2 0 - sin2 0.
sin 0 + sin 20
5. sin 0 cos 0. 6. cs +os20
cos 0 + cos 20 '
7. sin (r sin 0). 8. cos (w sin 0).
sin (r cos 0)
cos (7r sin O)'
sin 30
10. Trace the changes in the sign and magnitude of cos0 as the
angle increases from 0 to 90.2
angle increases from 0 to 90~.

L. T.

10