IB Maths AA Trigonometry: Unit Circle, Identities and Equations Without the Panic

For students coming from CBSE, ICSE or IGCSE, trigonometry in IB Analysis and Approaches is often the first real shock. Triangles are still there, but most marks come from the unit circle, identities and trig equations – usually in Paper 1, without a calculator. Students who make these automatic gain marks across the whole course, including calculus and complex numbers.

What AA SL covers

• Radians, arc length and sector area.
• The unit circle definitions of sin, cos and tan, and exact values for angles such as π/6, π/4 and π/3 in every quadrant.
• Identities: sin²θ + cos²θ = 1, tan θ = sin θ / cos θ, and the double-angle formulas for sin 2θ and cos 2θ.
• Graphs of sin, cos and tan, and transformed graphs such as y = a sin(b(x + c)) + d.
• Solving trig equations in a given interval, including quadratic-type equations.
• Triangle trigonometry: sine rule, cosine rule, area ½ab sin C, and the ambiguous case of the sine rule.

What AA HL adds

• Reciprocal functions: sec, cosec and cot, and identities such as 1 + tan²θ = sec²θ.
• Inverse trig functions (arcsin, arccos, arctan) and their graphs.
• Compound angle identities for sin(A ± B), cos(A ± B) and tan(A ± B), and the double-angle formula for tan.
• Harder equations and proofs combining several identities.

The Paper 1 traps

1. Missing solutions. "Solve sin x = ½ for 0 ≤ x ≤ 2π" has two answers. With 2x or 3x inside, there are more – adjust the interval first.
2. Dividing by a trig function (e.g. cos x) and losing the solutions where it equals zero. Factorise instead.
3. Wrong sign in a quadrant. Use the unit circle, not memory.
4. Degrees in a radians question (or the reverse).
5. Forgetting the ambiguous case in the sine rule – two possible triangles.

Making trigonometry automatic

• Draw the unit circle from memory once a day for two weeks, with exact values. After that it sticks.
• Learn identities by using them, not by reciting: rewrite one expression in three different ways.
• Use a "solve" routine: rearrange → find the base angle → use the unit circle for all quadrants → apply the interval.
• Sketch graphs to check how many solutions to expect before solving.
• Practise without a calculator – Paper 1 depends on it.

Where trigonometry appears later

• Calculus: derivatives and integrals of trig functions, and in HL, reciprocal and inverse functions.
• Complex numbers (HL): modulus–argument form and De Moivre's theorem.
• Vectors (HL): angles between lines and planes.

A weak trig foundation shows up in all of them.

How Maths Bodhi helps

• A diagnostic of exact values, identities and equation-solving in the first session.
• Unit-circle-first teaching, so students reason rather than memorise.
• Paper 1-style practice without a calculator, marked against the markscheme.
• For HL, structured work on reciprocal and compound-angle identities and proofs.

Ajay Vatsyayan (M.Tech, 14+ years teaching maths) teaches IB DP maths at Maths Bodhi and has taught students from schools across Gurgaon, including The Shri Ram School (Moulsari), Kunskapsskolan, DPS International and Suncity School. Maths Bodhi is independent and not affiliated with any school. Read Ajay's profile, or see our IB trigonometry tutor, AA SL and AA HL pages.

Home sessions across Gurgaon – including Golf Course Road and Sector 56 – or online. Book a free demo class.

Related: AA Paper 1 without a calculator, functions and transformations and the IB DP maths guide for Gurgaon families.

Topic lists checked against the current IB AA guide by the Maths Bodhi team (October 2026). Teaching approach reviewed by Ajay Vatsyayan.