Plane trigonometry, by S.L. Loney.

ANGLES OF ANY MAGNITUDE.

51

sin2 + cos20 = 1,
sin 6
s-i = tan 6,
Cos 0
sec26 = 1 +tan26,
and cosec20 = 1 + cot26.
52. Signs of the trigonometrical ratios.
First quadrant. Let the revolving line be in the first
quadrant, as OP1. This revolving line is always positive.
Here OM1 and MifP, are both positive, so that all the
trigonometrical ratios are then positive.
Second quadrant. Let the revolving line be in the
second quadrant, as OP2, Here MYP2 is positive and OM2
is negative.
The sine, being equal to the ratio of a positive quantity
to a positive quantity, is therefore positive.
The cosine, being equal to the ratio of a negative
quantity to a positive quantity, is therefore negative.
The tangent, being equal to the ratio of a positive
quantity to a negative quantity, is therefore negative.
The cotangent is negative.
The cosecant is positive.
The secant is negative.
Third quadrant. If the revolving line be, as OP3, in
the third quadrant, we have both iM3P3 and OM. negative.
The sine is therefore negative.
The cosine is negative.
The tangent is positive.
The cotangent is positive.
The cosecant is negative.
The secant is negative.
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