Trigonometry (Grade 12 NSC Matric Mathematics): Flashcards

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Compound Angle Identities
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Definition of compound angles

Expressions involving sum or difference of two angles

Distributive law for trig ratios

Does NOT apply: cos⁡(α−β)≠cos⁡α−cos⁡β\cos(\alpha - \beta) \neq \cos \alpha - \cos \beta

cos⁡(α−β)\cos(\alpha - \beta) formula

cos⁡αcos⁡β+sin⁡αsin⁡β\cos \alpha \cos \beta + \sin \alpha \sin \beta

cos⁡(α+β)\cos(\alpha + \beta) formula

cos⁡αcos⁡β−sin⁡αsin⁡β\cos \alpha \cos \beta - \sin \alpha \sin \beta

sin⁡(α−β)\sin(\alpha - \beta) formula

sin⁡αcos⁡β−cos⁡αsin⁡β\sin \alpha \cos \beta - \cos \alpha \sin \beta

sin⁡(α+β)\sin(\alpha + \beta) formula

sin⁡αcos⁡β+cos⁡αsin⁡β\sin \alpha \cos \beta + \cos \alpha \sin \beta

Sign pattern in cosine compound angle formulae

Sign matches the angle operation (+ stays +, - stays -)

Sign pattern in sine compound angle formulae

Sign opposite to angle operation (+ becomes -, - becomes +)

Co-function: cos⁡(90°−θ)\cos(90° - \theta)

sin⁡θ\sin \theta

Express 75°75° as sum of special angles

45°+30°45° + 30°

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