IB Mathematics AA HL – Trigonometric Functions (Module 6)

Advanced trigonometry for IB AA HL: graphs, identities, equations, inverses, modelling, and calculus

Created byKonstantinos Kokoris

Last updated 2/2026

English

What you'll learn

Understand trigonometric functions using the unit circle, exact values, and radians as required in IB Mathematics AA HL.
Analyse and sketch trigonometric graphs, including transformations, period, amplitude, and phase shift.
Solve trigonometric equations and identities with correct general solutions and domain restrictions.
Work confidently with inverse trigonometric functions and principal values in IB exam questions.
Apply trigonometric functions to modelling and calculus problems at HL level.

Course content

1 section • 14 lectures • 40m total length

Module overview1:27
Trigonometric Functions: Definition & Unit Circle4:01
Introduce sine, cosine, and tangent using the unit circle.
Define angles in radians and relate them to coordinates.
Connect right-triangle definitions with unit-circle values.
Identify exact trigonometric values at key angles.
Set the foundation for graphs, identities, and equations in IB AA HL.
Graphs of Trigonometric Functions3:58
Explore the graphs of sine, cosine, and tangent functions.
Understand amplitude, period, and key features of each graph.
Identify intercepts, maximum and minimum values, and asymptotes.
Link algebraic form to graphical behaviour.
Apply IB-style interpretation and sketching techniques.
Transformations of Trigonometric Graphs3:47
Learn how translations, stretches, and reflections affect trig graphs.
Understand the roles of parameters aaa, bbb, ccc, and ddd.
Analyse changes in amplitude, period, phase shift, and vertical shift.
Move confidently between equations and graphs.
Apply transformations in IB-style problems and interpretations.
Trigonometric Identities3:14
Understand the core trigonometric identities and where they come from.
Use identities to simplify expressions logically, not mechanically.
Prove identities step by step using valid algebraic reasoning.
Recognise which identities are useful in different IB-style contexts.
Avoid common traps in identity manipulation.
Solving Trigonometric Equations3:25
Learn a structured IB-safe method for solving trigonometric equations.
Find general solutions for sine and cosine using reference angles.
Handle equations with multiple solutions over given intervals.
Understand domain restrictions and common IB pitfalls in final answers.
Inverse Trigonometric Functions3:36
Understand inverse sine, cosine, and tangent with correct domains and ranges.
Interpret inverse trig graphs and principal values.
Solve equations involving inverse trigonometric functions.
Avoid common IB errors with restricted ranges and exact values.
Trigonometric Equations with Inverses3:18
Solve trigonometric equations involving inverse functions correctly.
Translate inverse expressions into standard trigonometric forms.
Apply domain and range restrictions consistently.
Avoid extraneous solutions in IB-style problems.
Trigonometric Modelling3:19
Model real-world periodic phenomena using trigonometric functions.
Interpret amplitude, period, phase shift, and vertical shift.
Construct equations from contextual data and graphs.
Solve IB-style modelling problems with clear mathematical justification.
Trigonometric Identities in Proof & Simplification3:20
Use core trigonometric identities to simplify expressions logically.
Prove identities using one-side-only, IB-approved methods.
Apply factoring and algebraic structure correctly.
Avoid common errors in identity manipulation and domain handling.
Calculus with Trigonometric Functions2:57
Differentiate and integrate trigonometric functions using radians.
Apply the chain rule correctly in trigonometric contexts.
Evaluate definite and indefinite integrals involving trig functions.
Solve IB-style calculus problems with clear structure and notation.
Worked IB-Style Examples (Exam Workshop)3:13
Final Exam0:07
Module Summary and Next Steps0:33

Requirements

Familiarity with basic algebra and functions at IB Mathematics SL level or equivalent.
Prior exposure to basic trigonometric ratios is recommended but not required.
All content is taught assuming angles are measured in radians.

Description

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 for further topics in the syllabus.

Students under the age of 18 may only access this course through an account created and managed by a parent or legal guardian, in accordance with Udemy’s policies.

Who this course is for:

IB Mathematics AA HL students who want a deep, exam-aligned understanding of trigonometric functions, identities, equations, modelling, and calculus.
IB Mathematics AA HL students who want a deep, exam-aligned understanding of trigonometric functions, identities, equations, modelling, and calculus.
Students who struggle with trigonometric structure, domains, and general solutions in IB exams.
Learners who want full IB-style solutions, not shortcut-based problem solving.
IB teachers looking for a structured reference aligned with examiner expectations.