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Class Notes – Trigonometry (Year 13 Maths)

September 19, 2026September 19, 2026 Navu

Reciprocal Trigonometric Functions

$sec$ $\theta$ $=$ $\frac{1}{cos\hspace{1 mm}\theta}$

$cosec$ $\theta$ $=$ $\frac{1}{sin\hspace{1 mm}\theta}$

$cot$ $\theta$ $=$ $\frac{1}{tan\hspace{1 mm}\theta}$

Trigonometric Identities

$1 + tan^2\hspace {1mm}\theta \equiv sec^2\hspace{1 mm}\theta$

$1 + cot^2\hspace {1mm}\theta \equiv cosec^2\hspace{1 mm}\theta$

Compound Angle Formulae:

$sin(A+B) \equiv sinAcosB + cosAsinB$

$sin(A-B) \equiv sinAcosB - cosAsinB$

$cos(A+B) \equiv cosAcosB - sinAsinB$

$cos(A-B) \equiv cosAcosB + sinAsinB$

$tan(A+B) \equiv \frac{tanA+tanB}{1-tanAtanB}$

$tan(A-B) \equiv \frac{tanA-tanB}{1+tanAtanB}$

Double Angle Formulae:

$sin2\theta \equiv 2sin\theta$ $cos\theta$

$cos2\theta \equiv cos^2\theta - sin^2\theta$

$cos2\theta \equiv 2cos^2\theta - 1$

$cos2\theta \equiv 1 - 2sin^2\theta$

$tan2\theta \equiv \frac{2tan\theta}{1-tan^2\theta}$

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