Game Development Reference
In-Depth Information
Figure 12.18
As you approach values at which the cosine reaches 0, the tangent values become undefined.
from points on the
x
coordinate at which cos
is 0. Such a curve occurs when the
value of the denominator becomes increasingly smaller. The tangent values in
turn become increasingly larger. The values increase indefinitely. This is known
as an asymptotic curve.
y
As Table 12.5 explains, you can formally state that certain values are undefined if
you say that tan
lacks definition at any value of
2
รพ
k
. The value of
k
is any
integer. In Figure 12.18, among the values of
x
defined in this way are
2
,
2
,
5
2
,
and
5
2
.
Plotting Cotangent Values
When you plot cotangent values on the Cartesian plane, as with tangent values,
at certain points you cannot define them. As the discussion in Table 12.5 indi-
cates, if the value of the sin
is 0, then the value of the cotangent is undefined.
When you plot cotangent values, the resulting curve rises indefinitely as it
approaches a line extending vertically from any point on the
x
coordinate at
which sin
is 0.
