Graphics Reference
In-Depth Information
cos(
A
±
B
)=cos(
A
)cos(
B
)
∓
sin(
A
) sin(
B
)
tan(
A
)
±
tan(
B
)
tan(
A
±
B
)=
1
∓
tan(
A
)tan(
B
)
sin(2
β
)=2sin(
β
)cos(
β
)
cos(2
β
)=cos
2
(
β
)
sin
2
(
β
)
−
cos(2
β
)=2cos
2
(
β
)
−
1
2sin
2
(
β
)
cos(2
β
)=1
−
4sin
3
(
β
)
sin(3
β
)=3sin(
β
)
−
cos(3
β
)=4cos
3
(
β
)
−
3cos(
β
)
cos
2
(
β
)=
1
2
(1 + cos(2
β
))
sin
2
(
β
)=
1
2
(1
−
cos(2
β
))
4.8 Perimeter Relationships
Finally, referring back to Figure 4.3, we come to the relationships that inte-
grate angles with the perimeter of a triangle:
S
=
1
2
(
a
+
b
+
c
)
=
(
s
sin
A
2
−
b
)(
s
−
c
)
bc
=
(
s
sin
B
2
−
c
)(
s
−
a
)
ca
=
(
s
sin
C
2
−
a
)(
s
−
b
)
ab
=
s
(
s
cos
A
2
−
a
)
bc
=
s
(
s
cos
B
2
−
b
)
ca
=
s
(
s
cos
C
2
−
c
)
ab