Angles - Measurements

• Angles - Definition
• Angles - Standard position

• Angles - Units - Conversion

• Circular arc - Length
• Sector of a Circle - Area

Trigonometry - Functions

• Trigonometric ratios - Definitions and signs
• Trigonometric ratios - Acute angles
• Trigonometric ratios - Standard angles
• Trigonometry - Identities - Standard

Allied angles

• Allied angles - (90 + A), (90 - A)
• Allied angles - (180 + A), (180 - A)
• Allied angles - (270 + A), (270 - A)
• Coterminal angles - Formulae and examples

Compound, multiple & submultiple angles

• Compound angles - Sum - Derivation
• Compound angles - Difference - Derivation

• Multiple angles - Formulae - 2A - Derivations
• Multiple angles - Formulae - 3A - Derivations
• Submultiple angles - Formulae - Derivations

• Transformation formulae - Examples

Trigonometric functions - Variation and Periodicity

• Variation - Explanation

• Trigonometric function - Periodicity - Values and examples

Trigonometric functions - Graphs

• Trigonometric functions - Graphs - Sine, cosine, tangent
• Trigonometric functions - Graphs - Cotangent, secant, cosecant

• Trigonometric functions - Extreme values - a cos A ± b sin A ± c

Heights and distances

• Heights and distances - Angle of elevation - Examples
• Heights and distances - Angle of depression - Examples

Properties of triangles

• Properties of triangle - Sine rule
• Properties of triangle - Projection rule
• Properties of triangle - Cosine rule
• Properties of triangle - Half angle formulae
• Properties of triangle - Tangent rule
• Properties of triangle - Area
• Properties of triangle - Area - Polygon and quadrilateral

Solution of triangles

• Triangle - Solution - Three sides given
• Triangle - Solution - Two sides and an angle given
• Triangle - Solution - Two angles and a side given
• Triangle - Solution - Ambiguous case

• Incircle and excircle - Theorems

Trigonometric functions - Inverse

• Inverse trigonometric functions - Properties - Sine, cosecant
• Inverse trigonometric functions - Properties - Cosine, secant
• Inverse trigonometric functions - Properties - Tangent, cotangent
• Trigonometric functions - Principal values - Finding

Trigonometric functions - Hyperbolic and inverse hyperbolic

• Trigonometric functions - Hyperbolic - Identities

• Trigonometric functions - Inverse hyperbolic - Logarithmic

Trigonometric equations - General solution - Methods & examples

• General solution - sin A = k, cos A = k and tan A = k
• General solution - sin A = 0, cos A = 0 & tan A = 0
• General solution - sin²A = sin²B, cos²A = cos²B and tan²A = tan²B
General solution - a cos A + b sin A = c.

Complex numbers - Operations & properties

• Complex numbers - Addition and difference
• Complex numbers - Product and division
• Complex numbers - Theorems and laws
• Complex numbers - Integral powers
• Complex numbers - Conjugate - Properties
• Complex numbers - Modulus - Properties

• Complex numbers - Argand diagram - Properties
• Complex numbers - Polar Form - Properties
• Complex numbers - Modulus and argument - Properties
• Complex numbers - Addition and subtraction - Argand plane
• Complex numbers - Multiplication and division - Argand plane

Complex numbers - De Moivre's theorem

• Complex numbers - De Moivre's theorem - Integral index
• Complex numbers - De Moivre's theorem - Rational index
• Complex numbers - nth roots - Extraction
• Complex numbers - Roots of unity - Cube and nth rational index

• Complex numbers - sin^n A to sine of multiples of A
• Complex numbers - cos^n A to cosines of multiples of A