Game Development Reference
In-Depth Information
After generating the graphs shown in Figure 12.22, generate other graphs using
the same approach. Here are some primary relationships to explore:
1
tan
y ¼
cot
y
1
cos
sec
y ¼
y
Conclusion
This chapter brings to an end your exploration of pre-calculus as presented in
this topic. Accordingly, you first reviewed the Pythagorean theorem and exam-
ined the standard right triangle. When you examined this triangle, you took a
close look at the ratio between the lengths of the sides of the triangle and how
they allow you to see how one of the most fundamental of the trigonometric
ratios, the sine, comes to life.
Having explored these beginnings, you then examined ways to measure angles.
While degrees provide a reliable approach to such measurements, radians often
prove easier to work with. A radian is the arc of a circle equal in length to the
radius of the circle. Using radian measures, you are able to express angles of a
circle and translate them to a Cartesian coordinate system that allows you to
plot different trigonometric values. Toward this end, you explored standard
graphs depicting cosine, tangent, cotangent, secant, and cosecant values. Such
values generate periodic graphs that can be understood if you consider a few key
points.
As is explained in the opening chapters of this topic, the intent has not been to
provide you with a comprehensive context in which to explore all the topics you
might explore in an examination of pre-calculus mathematics. Instead, the
intention is to provide you with points of contact that you can use to reacquaint
or familiarize yourself with some aspects of pre-calculus mathematics that might
benefit from an alternative type of presentation.
While successfully meeting the challenges a calculus course presents depends to a
great extent on systematically studying algebra and trigonometry, it remains that
viewing such studies in the context of a game leading to a bigger game puts you in
a position to gain much more satisfaction than you would otherwise from your
endeavors. To learn anything is a victory.
