Topic 3 – Core: Circular functions and trigonometry

Trigonometric Ratios

1. Trigonometric ratios for 30°, 45° and 60°

Trigonometric Graphs and Transformations

1. Trigonometric graphs
2. Translations of trig graphs
3. Reflections of trig graphs
4. Stretches of trig graphs
5. Combining transformations

Applications of Trigonometry

1. Exam Questions - Sine rule
2. Cosine rule
3. Arcs, sectors and segments

Trigonometric Equations

1. Quadrant rule to solve trig equations
2. Trig equations with different ranges
3. Trig equations with multiple angles
4. Trig equations that factorise

Trigonometric Identities

1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
3. Solving equations using identities

Sec θ, Cosec θ and Cot θ

1. Trig functions sec θ, cosec θ and cot θ
2. Graphs of sec θ, cosec θ and cot θ

Inverse trigonometric functions

1. Inverse trigonometric functions - arcsin x, arccos x, arctan x
2. Examples using Inverse trigonometric functions

Identities & Equations – Pythagorean Type

1. sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x

Identities – Addition type

Identities & Equations – Double angle type

1. Solving equations using double angle identities

Identities – Half angle type

Identities – Triple angle type

1. Identity for cos 3θ and sin 3θ