Plane trigonometry, by S.L. Loney.

TRIGONOMETRICAL RATIOS.

33

Hence OP2 = PP'2 = 4PM2 = 40P2 - 4a2,
where OM equals a.
3O. P302= 4a,
2a a
so that OP = and MP= lOP =
MiP 1.. sin 30 =opOM 2a /3
cos 30 = = aOP V3 2'
sin 300 1
and tan 30 = 30 =
cos 30~ /3'
35. Angle of 60~.
Let the angle AOP traced
out be 60~.
Take a point N on OA, so
that
MN = OM= a (say).
The two triangles OMP and
NMP have now the sides OM 6
O M N A
and MP equal to NM and MP N A
respectively, and the included
angles equal, so that the triangles are equal.. PN = OP, and zPNM = POM =60~.
The triangle OPN is therefore equilateral, and hence
OP = ON= 20M= 2a.. MP = VOP2- OM = V4a2- a2 = 3. a.

L. T.

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