GCSE Trigonometry

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)