Conclusion

This chapter brings to an end your exploration of pre-calculus as presented in this book. Accordingly, you first reviewed the Pythagorean theorem and examined 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 book, 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.

Memorizing rules and applying them in silent ways is a traditional approach to mathematics. Engaging in a gradually expanding discussion in which you continuously broaden your ability to voice what you know provides an alternative approach to the study of math. It is an approach often spoken about in classes involving students and others interested in developing games. It is the approach that forms the starting and ending points of this book. If such an approach enables you to have a greater sense that you can learn mathematics, then this book has served its purpose.