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TRIGONOMETRY. 155
Sin.2
+ cos.2 = radius2
.
Tang. 2
+ radius2 = secant2
.
Cot.2
+ radius2 = cosecant2
.
But the trigonometrical tables are calculated with radius
= 1, hence,
sin.2
+ cos.2 = 1.
tang.2
+ 1 = sec.2
cotang.2 -j- 1 = cosecant2
.
tang. = cosin.
1
tang,
secant
secant — cosin.
cotang. = cosin.
sin.
1
sin.
cosec. — sin.
sin.
cotang. = 1
tang.
cosin. = */\ — sin.2
cosin.
cotang.
tang.
sin.
1
cosec.
cosin.
cotang.
_ vr=
tang.
FIG. 15.
/ +
\
\
/^\ 1
Fig. 16. Fig. 17.
6 \
Z&
<N
^\
^n >
(P.
X^H i
Sine and Cosine of the Sum of Two Angles.
(See Fig. 15).
Sine (a + b) = sin. a X cos. b -f- cos. a X sin. b.
Cos. (a -j- b) = cos. a X cos. b — sin. a X sin. b.
Sine and Cosine of Twice any Angle.
(See Fig. 16).
Sin. 2« = 2X sin. a X cos. a.
Cos. 2 a.
= cos.2
a — sin.2
a.
Sine and Cosine of the Difference of Two Angles.
(See Fig. 17).
Sin. {a — b) = sin. a X cos. b — cos. a X sin. b,
Cosin. (a — b) = cos. a X cos. b + sin. a X sin. b.
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