Identities, reduction formulas, compound and double angles, sine rule, cosine rule and area rule for Grade 12 CAPS trigonometry, with NSC Paper 2 notes.
Trigonometry is the largest section of NSC Paper 2. The information sheet supplies the sine, cosine and area rules plus compound angle identities — the reduction formulas and special angles must be known.
| Formula | Expression | Note |
|---|---|---|
| Square identity | sin²θ + cos²θ = 1 | Rearranged forms are used in almost every proof. |
| Quotient identity | tanθ = sinθ / cosθ | Convert tan to sin/cos when simplifying. |
| Compound angles | sin(A ± B) = sinA cosB ± cosA sinB | Also cos(A ± B) = cosA cosB ∓ sinA sinB. |
| Double angles | sin2A = 2 sinA cosA; cos2A = 1 − 2sin²A | cos2A has three equivalent forms — choose the one matching the target expression. |
| Sine rule | a/sinA = b/sinB = c/sinC | Use when given two angles and a side, or two sides and a non-included angle. |
| Cosine rule | a² = b² + c² − 2bc·cosA | Use for three sides, or two sides and the included angle. |
| Area rule | Area = ½ ab·sinC | The angle must be between the two given sides. |
Some are printed on the official information sheet, but not all. Treat every formula on this page as examinable and learn it with a worked example so you recognise when to use it.
Trigonometry is examined in Paper 2 of the NSC Mathematics examination.
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