MYP Maths: The Sine & Cosine Rules (Extended) — FAQ

According to the IB's MYP: From Principles into Practice guide, non-right-angled trigonometry sits under Criterion D (Applying mathematics in real-life contexts) as much as Criterion A, because these rules are usually taught through navigation, surveying and construction problems rather than abstract triangles alone.

Quick tip: if you can draw a straight line from an angle to its opposite side and label both, sine rule works. If every angle you know is 'trapped' between two known sides, go straight to cosine rule.

Common mistake: students apply the sine rule to an SAS triangle because it looks simpler — but with no angle-opposite-side pair, the equation has two unknowns and can't be solved.

1. Draw the triangle, even roughly.
2. Mark every known side and angle.
3. Ask: is there an angle directly opposite a known side? If yes → sine rule.
4. If not, but you have SSS or SAS → cosine rule.
5. Solve, then sanity-check the answer looks like a sensible triangle (angles summing to 180°, longest side opposite largest angle).

Step-by-step:

1. Substitute values: a² = 8² + 10² − 2(8)(10)cos(55°)
2. Calculate cos(55°) ≈ 0.5736
3. a² = 64 + 100 − 91.78 = 72.22
4. a = √72.22 ≈ 8.50 cm (3 s.f.)

MYP assessment criteria reward showing this working under Criterion A (Knowing and understanding) — a bare answer without the substitution line often loses marks even if correct.

Step-by-step:

1. Write the rule with known values: 12/sin(40°) = b/sin(65°)
2. Cross-multiply: b = 12 × sin(65°) / sin(40°)
3. b ≈ 12 × 0.9063 / 0.6428 ≈ 16.92 cm

Common mistake: forgetting the angle sum rule to find the third angle (180 − 40 − 65 = 75°) before attempting the area, if the question asks for it later.

Example: if sin B = 0.75, your calculator returns B ≈ 48.6°, but B ≈ 131.4° is also mathematically valid. Check whether the second option makes the angle sum exceed 180° with the angles you already know — if it does, discard it. If not, both triangles may be genuine answers, and IB-style questions sometimes ask you to state both.

Common mistake: swapping b and c in the formula, or plugging in an angle from a previous part of the question instead of the one actually asked for. A quick fix — relabel the triangle from scratch before touching the calculator.

Schools set their own pathway (Standard or Extended) based on student readiness, so confirm directly with your child's maths teacher which content applies — the IB doesn't publish a single universal MYP exam paper the way DP does.

Quick tip: before any test, confirm your calculator is set to degrees, not radians — this is the single most common cause of wildly wrong answers in trigonometry tasks.

This is worth remembering for Criterion B (Investigating patterns) tasks — showing you understand why the cosine rule reduces to Pythagoras at 90° demonstrates genuine mathematical reasoning, not memorised formula substitution.

1. Drill rule-selection first, separate from solving — just sort 15 triangles into 'sine' or 'cosine' piles.
2. Then solve a mixed set, showing full substitution steps.
3. Review any wrong answers by checking whether the rule choice or the arithmetic was the problem — they need different fixes.

On RevisionPrep, Topical Worksheets group these by difficulty so you can drill rule-selection separately from calculation accuracy before mixing them together.

If your child can solve a triangle correctly when told which rule to use, but freezes on mixed practice, that confirms it's a recognition issue, not a maths-ability one — worth flagging to their teacher directly, since it's usually fixed within a couple of focused practice sessions rather than needing a syllabus-wide review.