Units 1 & 2 (Trigonometry Foundations & Applications)
Build a conceptual and procedural understanding of trigonometric ratios, exact values, and the unit circle. Develop fluency in solving right-angled and non-right-angled triangles using sine, cosine, and area rules. Extend to trigonometric functions, their graphs, identities, and applications in modelling periodic phenomena.

Unit 1: Trigonometric Ratios and the Unit Circle

1.1 Trigonometric Ratios in Right-Angled Triangles

• Definitions: sine, cosine, tangent as ratios

• Solving for unknown sides and angles using primary trig ratios

• Applications: angles of elevation/depression, bearings

1.2 Exact Values and Special Triangles

• 30°–60°–90° and 45°–45°–90° triangles

• Exact trig ratios for 0°, 30°, 45°, 60°, 90°

• Using rationalisation and simplification techniques

1.3 Introduction to the Unit Circle

• Definition: unit circle with radius 1

• Coordinates and symmetry for key angles

• Linking degrees and radians

• Signs of trig functions in quadrants (ASTC rule)

1.4 Graphs of Sine, Cosine, and Tangent Functions

• Sketching graphs over specified intervals

• Period, amplitude, and midline

• Transformations: vertical shifts, stretches/compressions, phase shifts

• Graphical interpretation of solutions to trig equations

Unit 2: Trigonometric Equations, Identities, and Applications

2.1 Solving Non-Right-Angled Triangles

• Sine Rule (ambiguous case considerations)

• Cosine Rule for sides and angles

• Area of a triangle using ½ab sin(C)

• Applications to navigation and surveying problems

2.2 Trigonometric Identities and Equations

• Pythagorean identities: sin²x + cos²x = 1

• Using identities to simplify and solve trig expressions

• Solving equations involving multiple angles, exact and approximate solutions

• Graphical verification using CAS technology

2.3 Modelling with Trigonometric Functions

• Real-world periodic phenomena: tides, seasons, sound waves

• Constructing sine and cosine models: identifying amplitude, period, and phase shift from context

• Interpreting models to make predictions or solve contextual problems