2.2 Game 2302-0320 brief trigonometry tutorial

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
• Discussion
  • Degrees versus radians
  • Sine, cosine, and tangent
    • The sine and arcsine of an angle
    • The cosine and arccosine of an angle
    • The tangent and arctangent of an angle
  • Dealing with quadrants
• Run the scripts
• Miscellaneous

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1 . Output for script in Listing 1.
• Figure 2 . A 3-4-5 triangle.
• Figure 3 . Output for script in Listing 2.
• Figure 4 . Output for script in Listing 3.
• Figure 5 . Interesting sine equations.
• Figure 6 . Interesting cosine equations.
• Figure 7 . Output for script in Listing 5
• Figure 8 . Two very important equations.
• Figure 9 . Interesting tangent equations.
• Figure 10 . Output for script in Listing 7.
• Figure 11 . Sinusoidal values at 90-degree increments.
• Figure 12 . Sinusoidal values at 45-degree increments.
• Figure 13 . Sinusoidal values at 22.5-degree increments.
• Figure 14 . Plot of cosine and sine curves.
• Figure 15 . Algebraic signs versus quadrants.
• Figure 16 . Output from the code in Listing 9.

Listings

• Listing 1 . Conversions between radians and degrees.
• Listing 2 . Arcsin of 3-4-5 triangle.
• Listing 3 . Finding length of the opposite side.
• Listing 4 . Arccosine of 3-4-5 triangle.
• Listing 5 . Finding the length of the adjacent side.
• Listing 6 . Arctan of 3-4-5 triangle.
• Listing 7 . Finding the length of the opposite side.
• Listing 8 . Sinusoidal amplitude versus angle.
• Listing 9 . A function to deal with quadrants.

General background information

Many of the computational requirements for an introductory physics course involve trigonometry. This module provides a brief tutorial on trigonometry fundamentals.

Sine, cosine, and tangent

There are many topics, such as identities, that are covered in an introductory trigonometry course that won't be covered in this module. Instead,this module will concentrate mainly on performing computations on right angles using the sine, cosine, and tangent of an angle.

If I find it necessary to deal with identities in a later module, I will come back and update this module accordingly.

Discussion

Degrees versus radians

The most common unit of angular measurement used by the general public is the degree. As you are probably aware, there are 360 degrees in a circle.

The most common unit of angular measurement used by scientists and engineers is theradian.

(If you would like more background on radians, go to (External Link) .)

Conversions between radians and degrees

You may or may not be aware that one radian is equal to approximately 57.3 degrees. It is easier to remember, however, that 180 degrees is equal to PIradians where PI is the mathematical constant having an approximate value of 3.14159. We will use this latter relationship extensively to convert fromdegrees to radians and to convert from radians to degrees while working through the exercises in these modules.