IB Math AI SL 3.8 - Trigonometric Identities

This IB Math AI HL 3.8 – Trigonometric Identities slide deck deepens students’ understanding of trigonometry by connecting algebraic identities to geometric reasoning on the unit circle. The lesson begins by defining sine and cosine in terms of the unit circle and uses this framework to logically derive the Pythagorean identity, helping students see why the identities work, not just how to apply them.

Students are guided through the development and use of key identities, including double-angle formulae, with clear visual proofs and structured explanations. The lesson also extends the sine rule to explore the ambiguous case, highlighting when multiple triangle solutions are possible and how to interpret them correctly. Graphical methods for solving trigonometric equations within a finite interval further strengthen conceptual understanding and problem-solving fluency.

With its emphasis on visual justification, careful reasoning, and exam-focused practice, this slide deck supports advanced classroom learning and independent study, equipping HL students with the tools needed to confidently handle trigonometric identities and applications in IB assessments.