Syllabus Map

AA HL Geometry & Trigonometry Syllabus Points

The official IB syllabus content covering AHL points 3.9 through 3.14:

  1. 3.9Compound angle identities: $\sin(A \pm B), \cos(A \pm B), \tan(A \pm B)$; double angle formulas for tan
  2. 3.10Reciprocal functions $\sec\theta, \csc\theta, \cot\theta$ and identities ($1+\tan^2\theta=\sec^2\theta$); inverse trigonometric functions $\arcsin x, \arccos x, \arctan x$, domains, ranges, graphs
  3. 3.113D Vectors: component form $\mathbf{v} = v_1\mathbf{i} + v_2\mathbf{j} + v_3\mathbf{k}$, unit vectors, magnitude, scalar product $\mathbf{v}\cdot\mathbf{w}$, angle between vectors, perpendicularity
  4. 3.12Vector equations of a line in 3D: $\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}$; parametric and Cartesian forms; coincident, parallel, intersecting, and skew lines
  5. 3.13Vector cross product $\mathbf{v} \times \mathbf{w}$, geometric interpretation, area of parallelograms and triangles
  6. 3.14Equations of planes in 3D: $\mathbf{r}\cdot\mathbf{n} = \mathbf{a}\cdot\mathbf{n}$, Cartesian $ax+by+cz=d$; intersections of lines and planes, intersection of planes, angles

Study by topic

AHL Topic 3 Interactive Study Guides

Each guide is equipped with our standard 4-tab interface: Study Notes (theory, 3D diagrams & worked proofs), Practice Exercises (10 tiered problems with collapsible solutions), Formula Sheet, and Mini Test (MCQs & exam FRQs).

3.10 Reciprocal & Inverse Trigonometric Functions Study $\sec x, \csc x, \cot x$ identities, restricted domains and ranges for $\arcsin, \arccos, \arctan$, graphs, and exact trigonometric equations. Open Interactive Guide 3.9 Compound & Double Angle Identities Algebraic proofs and exact-value calculations using addition formulas for sine, cosine, and tangent, double angle expansions, and harmonic linear combinations $R\cos(x \pm \alpha)$. Open Interactive Guide 3.11 3D Vectors & The Scalar Product Component vectors in $\mathbb{R}^3$, magnitude, unit vectors, the scalar (dot) product $\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos\theta$, orthogonality tests, and vector projections. Open Interactive Guide 3.12 Vector Equations of Lines in 3D Vector and parametric equations of lines $\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}$, determining whether two lines in 3D are parallel, intersecting, coincident, or skew. Open Interactive Guide 3.13, 3.14 Vector Cross Product & Equations of Planes The cross product $\mathbf{u} \times \mathbf{v}$, normal vectors, vector equation of a plane $\mathbf{r}\cdot\mathbf{n} = d$, line-plane intersections, and angles between intersecting planes. Open Interactive Guide

Prerequisite Knowledge

Core SL Foundation Prerequisites

Review the 6 standard level Topic 3 guides:

3.1–3.3 Triangle Trigonometry & 3D 3.4 Circles & Radians 3.5 Exact Values & Ambiguity 3.6 Trig Identities SL 3.7 Trig Functions & Graphs 3.8 Solving Trig Equations