Game Development Reference
In-Depth Information
Figure 12.19
As you approach point values at which the sine reaches 0, the cotangent values become undefined.
A formal way to say this is that cot
. The
value of
k
can be any integer. Given this situation, as Figure 12.19 illustrates, such
values are 0,
is not defined at any value of
รพ
k
p
,2
p
,3
p
,
,
2
p
.
Plotting Secant Values
The value of the secant is undefined when it falls on a vertical line passing
through a point on the
x
axis at which the cosine value is 0. The cosine and secant
functions are reciprocals of each other.
When you plot a secant value, if you begin on the
x
axis at 0, the value of the
secant is 1. As you move toward
2
from 0, the value of the secant rises on an
asymptotic basis. In other words, it approaches
2
but never reaches it, and its
value becomes infinitely large.
After passing
2
, you are in the next phase of the secant. At this point, the secant
values shift to below the
x
axis. They start at an infinitely negative value, and then
increase in the range that is greater than
2
. The increase continues until you reach
the value of the secant is
1. Then values begin to infinitely decrease as
they near
3
2
. To complete the period, the secant values shift to above the
x
axis.
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