Graphics Reference
In-Depth Information
10
h
50
b
Fig. 4.2.
h and b are unknown.
h
= 10 sin(50
◦
)=10
×
0
.
76601
h
=7
.
66
b
10
=cos(50
◦
)
b
= 10 cos(50
◦
)=10
×
0
.
64279
b
=6
.
4279
4.3 Inverse Trigonometric Ratios
As every angle has its associated ratio, functions are required to convert one
into the other. The sin, cos and tan functions convert angles into ratios, and
the inverse functions sin
−
1
,
cos
−
1
and tan
−
1
convert ratios into angles. For
example, sin(45
◦
)=0
.
707, therefore sin
−
1
(0
.
707) = 45
◦
. Although the sin and
cos functions are
cyclic
functions (i.e. they repeat indefinitely) the inverse
functions return angles over a specific period.
4.4 Trigonometric Relationships
There is an intimate relationship between the sin and cos definitions, and the
are formally related by
cos(
β
)=sin(
β
+90
◦
)
Also, the theorem of Pythagoras can be used to derive other formulae such as
sin(
β
)
cos(
β
)
= tan(
β
)
sin
2
(
β
)+cos
2
(
β
)=1
1+tan
2
(
β
) = sec
2
(
β
)
1+cot
2
(
β
) = cosec
2
(
β
)
