Game Development Reference
In-Depth Information
1
x
α
1
x
2
Figure B.2. A triangle representing the inverse sine function.
1
x
2
we know that the third side of the triangle has length
, we can derive the
sin
1
x
values of the other trigonometric functions at the angle
as follows.
(
)
1
2
cos sin
x
=−
1
x
x
(
)
1
tan sin
x
=
(B.18)
2
1
x
Applying the same technique for the inverse cosine and inverse tangent func-
tions, we have the following.
(
)
1
2
sin cos
x
=−
1
x
2
1
x
(
)
1
tan cos
x
=
x
x
(
)
sin tan
1
x
=
2
x
+
1
1
(
)
1
cos tan
x
=
(B.19)
2
x
+
1
B.6 Laws of Sines and Cosines
Consider the triangle shown in Figure B.3 and observe the following.
z
α c
y
β c
sin
=
sin
=
(B.20)
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