Topic 8 of 11 · Form 3
Trigonometry
Pythagoras' theorem a² + b² = c²; SOH CAH TOA; angles of elevation and depression; bearings (three-figure, measured clockwise from north).
Notes for this topic 1 file, in order
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Right-angled triangles
Pythagoras' theorem a² + b² = c²; SOH CAH TOA; angles of elevation and depression; bearings (three-figure, measured clockwise from north).
Non-right-angled triangles
- Sine rule: a/sin A = b/sin B = c/sin C (ambiguous case when finding an angle).
- Cosine rule: a² = b² + c² − 2bc cos A.
- Area = ½ab sin C.
Worked example: In triangle ABC, a = 7 cm, b = 9 cm and C = 60°. Find c and the area.
c² = 49 + 81 − 126 × 0.5 = 67 → c = 8.19 cm
Area = ½ × 7 × 9 × sin 60° = 27.3 cm²
Trigonometry in 3D
Find lengths and the angle between a line and a plane by identifying right-angled triangles.
Trigonometric graphs
Graphs of sin x, cos x and tan x from 0° to 360°; solving sin x = k for two values.
Worked example: Solve sin x = 0.5 for 0° ≤ x ≤ 360°.
x = 30° or 150°
Check yourself
- A ladder 5 m long reaches 4 m up a wall. How far is its foot from the wall?
- The bearing of B from A is 070°. Find the bearing of A from B.
- Find angle A if a = 5, b = 6, c = 7.
Show answers
- 3 m
- 250°
- cos A = (36 + 49 − 25)/84 = 0.714 → A = 44.4°
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