Teaching resource · GCSE's · PDF
GCSE Trigonometry
Pupils progress from right-angled SOHCAHTOA through exact values to Sine/Cosine Rules for any triangle. Builds spatial reasoning, exact-value fluency, and multi-step problem-solving for Higher Tier exam questions.
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What this is
Topic: Trigonometry — Sine, Cosine & Tangent (Right-Angled & Non-Right-Angled Triangles)
Duration: 1.5 hours | Spec Ref: AQA 10.1–10.4, Edexcel 10.01–10.04 | Higher Tier
Prior Knowledge: Pythagoras’ theorem, angle facts, rearranging formulae, surds
Learning Objectives:
• Use SOHCAHTOA to find missing sides and angles in right-angled triangles
• Recall and apply exact trig values for 0°, 30°, 45°, 60°, 90°
• Apply the Sine Rule and Cosine Rule to non-right-angled triangles
• Calculate the area of a triangle using ½ab sin C
Starter (10 mins) — ‘Pythagoras Relay’:
5 quick Pythagoras problems (finding hypotenuse and shorter side). Recap: when do we NEED trig? When we have angles, not just sides. Show a triangle where Pythagoras alone can’t help.
Main Activity 1 (20 mins) — SOHCAHTOA:
• Label: Opposite, Adjacent, Hypotenuse relative to the angle
• sin θ = O/H, cos θ = A/H, tan θ = O/A
• Finding a side: identify ratio, substitute, rearrange
• Finding an angle: use inverse trig (sin⁻¹, cos⁻¹, tan⁻¹)
• Pupils work through 8 graduated examples on Worksheet 1 Section A
Main Activity 2 (15 mins) — Exact Trig Values:
• Derive from equilateral triangle (30/60) and isosceles right triangle (45)
• Table: sin/cos/tan for 0°, 30°, 45°, 60°, 90°
• Practice: solve triangles using exact values (leave answers as surds)
• Mini-whiteboard quiz: flash angle, pupils show exact value
Main Activity 3 (25 mins) — Sine Rule & Cosine Rule:
• Sine Rule: a/sin A = b/sin B = c/sin C (finding sides and angles)
• Ambiguous case awareness (two possible triangles)
• Cosine Rule: a² = b² + c² - 2bc cos A (finding sides); rearranged for angles
• Decision tree: which rule? (2 sides + included angle → Cosine; 2 angles + side → Sine)
• Area = ½ab sin C: when and why
• Pupils work through Worksheet 1 Section C
Plenary (15 mins) — ‘Real-World Trig’:
Bearings problem: a ship sails 12 km on bearing 065° then 8 km on bearing 140°. Find distance from start. Pupils sketch, identify triangle type, choose method. Exit ticket: 3 quick questions (one SOHCAHTOA, one exact value, one Sine/Cosine Rule).
Differentiation:
• Support: SOHCAHTOA only; labelling scaffolds; calculator-based; structured formula triangles
• Stretch: 3D trigonometry; angles of elevation/depression in multi-step problems; prove sine rule from area formula; trigonometric identities (tan = sin/cos, sin²+cos²=1)
What you get
Resources: Scientific calculators, protractors, Worksheet 1 & 2, exact values reference card, 3D shape models
Assessment: Exit ticket; Worksheet 2 multi-step problems; peer-mark exact values quiz
Cross-spec note: Both boards require exact values at Higher. AQA may embed in algebraic proof. Edexcel favours multi-step bearing/3D problems.
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