This is a beta course, so its structure, chapters, and examples may continue to change.
Trigonometric Functions
Trigonometric functions describe periodic relationships between angles and side ratios. They appear everywhere—from waves and oscillations to signal processing, navigation, and geometry.
Throughout this chapter, angles are measured in radians unless stated otherwise. One full circle is radians, so regularly appears in periods and identities.
What You Will Learn
- Angles and Radians — why we switch from degrees to radians, and how to convert between them.
- The Six Functions — sine, cosine, tangent, cotangent, secant, and cosecant: definitions, domains/ranges, graphs, and periodicity.
- Origins and History — how sine evolved from ancient Babylonian chord tables through Indian and Arabic astronomy to its modern name.
- Power Formulas — identities that rewrite powers of sine and cosine, useful for integration and simplification.
Chapter Sections
- Angles and Radians
- The Origin and Discovery of Trigonometric Functions
- Sine Function
- Cosine Function
- Tangent Function
- Cotangent Function
- Secant Function
- Cosecant Function
- Power Trigonometric Functions
- Power Reduction Formulas
Start with Angles and Radians if you have not yet seen why radians make calculus formulas clean.