IB Maths: Trigonometric Identities & Equations FAQ

It's the AA/AI syllabus strand covering the Pythagorean identity, double-angle formulae, and solving trig equations over a given domain. According to the IB, the current Mathematics guide (first exams 2021, still current for 2025 sessions) places this in Topic 3 (Geometry and Trigonometry). It's examined in Paper 1 (non-calculator, AA) and Paper 2 (calculator) as both short and extended-response questions.

You need the Pythagorean identity (${\sin }^2\theta +{\cos }^2\theta =1$) and its two rearrangements, the double-angle formulae for sine, cosine (three forms) and tangent, and — for AA HL only — compound-angle formulae and the identity $\tan \theta =\frac{\sin \theta }{\cos \theta }$. Most are given in the formula booklet, but you must know when to apply each.

Analysis & Approaches (AA) goes further into pure trig — compound-angle formulae, harder identity proofs, and trig equations requiring algebraic manipulation before solving. Applications & Interpretations (AI) sticks closer to modelling: trig functions describing periodic real-world data, with less emphasis on proving identities from scratch.

Find the reference (principal) solution first, then use the symmetry of the unit circle to generate every other solution within the stated domain — don't just add the period once and stop. Sketching even a rough graph of the function over the domain catches missing or extra roots before you submit an answer.

Look at what you're solving for. If the equation ends up with both $\sin x$ and $\cos 2x$ (or similar mixed terms), pick the version of $\cos 2x$ that rewrites everything in terms of the single function already present — usually $\cos 2x=1-2{\sin }^{2}x$ if $\sin x$ dominates the equation.

The top three, from years of marking mocks: forgetting extra solutions when the domain is wider than 0 to 360°/2π; treating ${\sin }^{2}x$ and $\sin x^2$ as the same thing; and substituting an identity but not simplifying fully, leaving an equation that looks unsolvable when it isn't.

Don't just re-read the formula list — that's the weakest form of revision for this topic. Work through past-paper questions by hand, timed, then mark your own script against the actual mark scheme to see exactly where method marks were lost, not just whether the final answer was right.

Yes — HL trig questions typically combine identities with calculus (differentiating trig functions) or require multi-step algebraic manipulation before an equation becomes solvable, while SL questions test identities and equations more directly. HL also examines compound-angle formulae, which SL does not.

It varies by paper and session, but a single trig equation question typically carries 4 to 8 marks in Paper 1 or Paper 2, and trig content also appears embedded inside larger calculus or vector questions worth considerably more. It rarely appears as a single isolated mark-heavy question at HL.

Almost always a domain-restriction slip. Students solve correctly for the principal value, then forget the trig function repeats — sine and cosine repeat every $2\pi$, tangent every $\pi$ — so a domain of $0$ to $4\pi$ can double your expected number of solutions compared with $0$ to $2\pi$.

If the difficulty is with algebraic proof and manipulation specifically, Applications & Interpretations (AI) usually asks less of that in this topic and leans on modelling instead. If the struggle is more general maths anxiety, switching routes won't fix it — the underlying issue needs addressing regardless of course.

Past IB papers marked against the official mark scheme are the gold standard, since they show exactly how method marks are awarded, not just final answers. Topic-specific worksheets that isolate trig equations from the rest of the syllabus also help — students often understand an identity in isolation but freeze when it's mixed into a longer, unfamiliar question.