Game Development Reference
In-Depth Information
Figure 12.13
A unit circle allows you to relate angles and arcs.
still the case that the same set of values can be used to map the arc. When you
factor 4
radians, you find that the terminal side of the angle rests on the
x
axis, as
does the terminal angle of 6
or 8
radians. The same holds true for all the other
angles that are multiples of 2
as well. As the arc rotates around the circle, it visits
the same points over and over. While the length of the arc grows, factoring allows
you to understand the arc in terms of a stable set of radian and degree values.
Figure 12.14 illustrates inner and outer rings surrounding a unit circle. The inner
ring shows you the coordinate values of the points on the perimeter of the unit
circle. The outer ring displays radian values associated with the plotted points.
Plotting Sine Values
Figure 12.15 illustrates what happens if you calculate the sine values of the angles
depicted in Figure 12.14. To make it so that the graph provides a fuller repre-
sentation of the way that the values fluctuate from positive to negative, the range
has been extended beyond that of a single rotation of a circle. The extension of
the range does not affect the overall pattern.
