IB Maths: Trigonometric Ratios & the Unit Circle — FAQ

It's tested across both papers: Paper 1 (non-calculator) asks for exact values from the unit circle and identity manipulation, while Paper 2 uses trig in modelling contexts with a GDC. According to the IB Mathematics AA and AI guides (first exams 2021, current for 2025), unit circle definitions underpin the whole trigonometry topic in both subjects.

The unit circle is a circle of radius 1 centred at the origin, where any point on it is $(\cos \theta ,\sin \theta )$ for angle $\theta$ measured anticlockwise from the positive x-axis. IB Maths uses it because it extends trig ratios beyond right-angled triangles to any angle, including negative and reflex ones.

You need to know the exact values at multiples of 30° and 45° (0, π/6, π/4, π/3, π/2 and their reflections) cold — no formula booklet entry gives you these. Everything else, like general identities, is in the IB formula booklet, so memorise the values, not the whole page.

Degrees and radians are two ways of measuring the same angle: 360° equals $2\pi$ radians, so 180° = $\pi$, 90° = $\pi /2$, and so on. IB Maths expects fluency in both, but radians are compulsory once you reach calculus with trig functions, since derivatives like $\frac{d}{dx}\sin x=\cos x$ only hold in radians.

Yes, generally — AA treats trig more algebraically, with proof-based identity work and unit circle reasoning expected without a calculator, while AI leans on the GDC and applies trig mostly to real-world modelling. If your child finds abstract algebra straightforward, AA's trig is manageable; if not, AI's applied approach usually suits better.

SL covers unit circle definitions, the Pythagorean identity, and solving simple trig equations over a given domain. HL adds compound angle formulae, double angle identities used in proof, and reciprocal trig functions (sec, csc, cot) that SL students never need to derive.

There's no fixed quota published by the IB, but trigonometry typically contributes a meaningful chunk of Paper 1 and Paper 2 marks each session, often appearing in at least one full multi-part question plus smaller items elsewhere. It also resurfaces inside calculus and vectors questions, so its real weighting is higher than a single topic tally suggests.

This almost always comes from forgetting that sine and cosine repeat every $360°$ (or $2\pi$), so an equation like $\sin x=0.5$ has multiple valid answers within a given domain, not just one. Always sketch the graph or unit circle first, mark the domain boundaries, then find every solution inside it.

Use the CAST rule: going anticlockwise from quadrant 1, All ratios are positive, then Sine, then Tangent, then Cosine are positive in each successive quadrant. It's a quick mental check before you commit to a sign in any exact-value or equation question.

The three I see most often as an examiner: mixing up degree and radian mode on the GDC, forgetting negative solutions when a domain includes negative angles, and misreading which axis gives sine versus cosine. All three are avoidable with a 10-second mode check and a quick circle sketch before answering.

Start by rebuilding the unit circle from scratch without looking it up — if you can derive every exact value from the two special triangles, you understand it rather than just recalling it. Then move to past-paper style equations with restricted domains, since that's where most marks are actually lost.

Yes, reasonably so — trig isn't an isolated topic; it reappears inside calculus, vectors and modelling questions right through to the final exam. A shaky grasp of the unit circle in Year 1 tends to resurface as lost marks in Year 2 topics that assume it's already automatic.

AI SL's trigonometry is generally considered more accessible since it's calculator-supported and framed around real contexts like tides or Ferris wheels, whereas AA SL expects exact-value fluency and some algebraic proof without a calculator. Neither is trivial, but AI asks for less abstract manipulation.