The text explains trigonometric functions, particularly sine, cosine, and tangent, and their visual representation using a unit circle. It discusses radians as an alternative to degrees for measuring angles. The concept of the dot product is introduced as a way to calculate the cosine of an angle between vectors. It also touches on methods for approximating trigonometric functions in software, including lookup tables, Taylor series, and range reduction. The text provides insights into how hardware and libraries compute these functions and suggests further resources for understanding the topic.
Here are the key facts extracted from the text:
1. Trigonometric functions involve right-angle triangles and are labeled with Greek letters.
2. The famous formulas are: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tan equals opposite over adjacent.
3. Radians are used to measure angles, with a circle being 2π radians instead of 360 degrees.
4. The dot product of two unit vectors gives cos Theta, representing the horizontal distance.
5. Lookup tables were historically used for trigonometric function approximations in games.
6. Various methods are employed to compute trigonometric functions, including range reduction, approximation, and reconstruction.
7. Symmetry is exploited to simplify the computation of trigonometric functions.
8. Hardware and libraries implement trigonometric functions using different methods, including polynomial approximations.
9. There are available resources for understanding trigonometry and math for game development.
These facts provide a concise summary of the information in the text without including opinions.