In our introductory lecture, Dr. Snellman presents the fundamentals of trigonometry, beginning with its real-world applications like noise-canceling headphones and moving into core concepts of right triangles and the Pythagorean theorem. We examine the six trigonometric functions and their relationships to the sides of right triangles, and demonstrate practical problem-solving techniques through examples. The lecture sets up future discussions on understanding trigonometric functions as mathematical functions independent of triangles.

In lecture two, we study the relationships between trigonometric functions, right triangles, and the unit circle. We examine the Pythagorean identity and its derivation, and discuss how the unit circle provides a geometric interpretation of trigonometric functions. The lecture concludes with a look at a table of values for all six trigonometric functions at standard angles (0°, 30°, 45°, 60°, 90°), including their radian measures, which form the foundation for understanding the unit circle.

In lecture three, we continue with the unit circle, exploring its properties, the trigonometric functions it represents, and techniques for generating its values without memorizing every point. We examine how to solve trigonometric equations using the unit circle and algebraic methods, and highlight the limitations of these approaches and the need for inverse trigonometric functions. The lecture concludes by introducing the concepts of even and odd functions in the context of cosine and sine.