IB Mathematics: AA SL topic guide

Geometry and Trigonometry

Geometry and Trigonometry is a core part of IB Mathematics: AA SL. This guide connects the syllabus ideas behind Introduction to Geometry and Trigonometry, 3D Geometry and Mensuration, The Sine Rule and Cosine Rule, Radian Measure and the Unit Circle, Trigonometric Identities and Graphs and 1 more units, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.

What you will learn

Geometry and Trigonometry syllabus outline

The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.

3.0

Introduction to Geometry and Trigonometry

What You Will Learn in Geometry and Trigonometry

3.1

3D Geometry and Mensuration

Distance & Midpoint in 3D · Volume, Surface Area & Angles in 3D Solids

3.2

The Sine Rule and Cosine Rule

The Sine Rule · The Cosine Rule & Area of a Triangle

3.3

Radian Measure and the Unit Circle

Radians, Arc Length & Sector Area · The Unit Circle & Exact Values

3.4

Trigonometric Identities and Graphs

The Pythagorean Identity · Graphs of Trig Functions & Transformations

3.5

Solving Trigonometric Equations

Solving Trig Equations Graphically & Analytically · Trigonometric Equations with Multiple Angles and Domains

Free worked preview

What You Will Learn in Geometry and Trigonometry

This complete preview comes from the Introduction to Geometry and Trigonometry unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.

Introduction to Geometry and Trigonometry

Geometry and trigonometry in Math AA is not a memorisation exercise for area formulas — it is the study of space, shape, and periodic behaviour, grounded in precise algebraic reasoning. You begin concretely: distances in 3D, volumes of solids, and the sine and cosine rules that liberate you from right-angled triangles. From there, the unit circle reframes sine and cosine as coordinates of a point — a geometric insight that extends trigonometry to any angle and makes the periodic nature of these functions immediately visible. At HL, vectors complete the picture by giving you an algebraic system for describing lines, planes, and their intersections in space. The trigonometric functions you study here reappear throughout calculus (their derivatives, their integrals, their Maclaurin series) and in the modelling of oscillatory phenomena, making this section as much a foundation for later work as it is a destination in itself.
Section Map — What Is Covered
  • 3D Geometry and Mensuration (3.1): distance and midpoint in space, volumes and surface areas of cones, spheres, and pyramids, and finding angles between lines and planes in solids
  • The Sine Rule and Cosine Rule (3.2): solving any triangle — plus the trigonometric area formula frac12absinC\\frac12 ab\\sin C — and handling the ambiguous case (SSA)
  • Radian Measure and the Unit Circle (3.3): why radians make arc length l=rthetal=r\\theta and sector area A=frac12r2thetaA=\\frac12 r^2\\theta elegantly simple, and the unit circle as the geometric definition of sine and cosine for any angle
  • Trigonometric Identities and Graphs (3.4): the Pythagorean identity sin2theta+cos2theta=1\\sin^2\\theta+\\cos^2\\theta=1 and the amplitude-period-phase-shift analysis of the general form y=asin(b(x−c))+dy=a\\sin(b(x-c))+d
  • Solving Trigonometric Equations (3.5): finding all solutions in a finite interval — not just the principal value your calculator returns — including equations with multiplied angles and quadratics in sin or cos
  • Further Trigonometric Identities (3.6, HL): compound-angle formulas, double-angle identities including the three equivalent forms of cos(2theta)\\cos(2\\theta), and the reciprocal functions sec, csc, and cot
  • Inverse Trigonometric Functions (3.7, HL): arcsin, arccos, arctan — their restricted domains and ranges, and why arcsin(sin150degree)\\arcsin(\\sin 150\\degree) equals 30°, not 150°
  • Vectors (3.8–3.10, HL): from representation and basic operations through the scalar product (angles, perpendicularity) and vector product (normal vectors, areas), to the vector equations of lines and planes in 3D
How to Approach This SectionDraw. Every single time. Whether it is a triangle with sides and angles labelled, a point on the unit circle with its coordinates, or two vectors with the angle between them marked — a sketch transforms abstract algebra into something your visual brain can process. For trigonometric equations, the CAST diagram or the symmetry of the sine/cosine graphs is your most reliable ally: your calculator will give you exactly one answer, but the question expects all of them within the given interval. When you reach vectors at HL, the central insight is that direction matters as much as magnitude — two vectors can have the same length but different directions, and the dot product measures precisely how aligned they are (vecucdotvecv=0\\vec{u}\\cdot\\vec{v}=0 is the condition for perpendicularity). The cross product, meanwhile, constructs the vector perpendicular to both inputs, which is how you build a normal vector to a plane — the single most important step in plane geometry problems.

Use the formulas

Keep the formula booklet beside you

Revision becomes faster when you practise locating the right equation and understand what every variable means. The full reference is public and searchable on any device.

Open IB Math AA SL Formula Booklet →

Reviewed by the Study to Learn editorial team · Updated 2026-07-24