IB Mathematics AA HL – Trigonometric Functions (Module 6)

About this course

This module covers trigonometric functions at true IB Mathematics AA HL level, with emphasis on structure, justification, and examiner expectations.Trigonometry is a core topic in IB exams, but many students struggle not because of formulas, but because of unclear reasoning, incorrect general solutions, and poor handling of domains, ranges, and principal values. This module is designed to address exactly those weaknesses.The course begins with precise definitions using the unit circle and radians, before moving to trigonometric graphs and transformations. Students learn how amplitude, period, phase shift, and vertical translations are identified and communicated clearly, as required in IB marking schemes.A significant part of the module is dedicated to trigonometric identities and equations. The focus is not on memorisation, but on logical structure: when an identity is valid, how it should be proven, and how solutions are written correctly within a given interval. Common IB pitfalls are addressed explicitly.Inverse trigonometric functions are treated carefully, with full attention to restricted domains, ranges, and principal values. These ideas are then applied to trigonometric equations involving inverse functions, an area where marks are often lost.The module also includes trigonometric modelling and calculus. Students learn how trigonometric functions are used to model periodic behaviour and how differentiation and integration with trigonometric functions are handled at HL level.Each section includes worked IB-style examples written exactly as they should appear in an exam script, followed by structured practice and a full module test.This module is part of a coherent IB Mathematics AA HL pathway, designed for students who want depth, clarity, and consistency in their exam preparation.This course is part of a structured IB Mathematics AA HL pathway and is designed to function both as a standalone module and as preparation f

Course objectives

• improve reasoning skills in trigonometry
• prepare for common pitfalls in IB assessments
• provide structured exam-style practice