Global Positioning System Reference
In-Depth Information
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Napier Analogies—not all permutations listed
cos
α − β
2
cos
α + β
2
tan
a
+
b
tan
c
2
=
(A.14a)
2
sin
α − β
2
sin
α + β
2
tan
a
−
b
tan
c
2
=
(A.14b)
2
cos
a
−
b
tan
α + β
2
cot
2
2
[34
=
(A.15a)
cos
a
+
b
2
Lin
—
7.0
——
Sho
*PgE
sin
a
−
b
tan
α − β
2
cot
2
2
=
(A.15b)
sin
a
+
b
2
Half Angle Formulas
s
=
(a
+
b
+
c)/
2
(A.16)
[34
sin
(s
−
a)
sin
(s
−
b)
sin
(s
−
c)
k
=
(A.17)
sin
s
tan
2
=
k
sin
(s
(A.18)
−
a)
tan
2
=
k
sin
(s
(A.19)
−
b)
tan
2
=
k
sin
(s
(A.20)
−
c)
Ha
lf Side Formulas
σ =
(
α + β + γ
)/
2
(A.21)
cos
(
σ − α
)
cos
(
σ − β
)
cos
(
σ − γ
)
k
=
(A.22)
−
cos
σ
