Units 1 & 2 (Circular Functions)
Explore the unit circle definition of trigonometric functions, their algebraic representations, and graphical behavior. Emphasis is placed on understanding sine, cosine, and tangent as periodic functions, solving trigonometric equations, and applying these functions in modelling and geometric contexts.

Unit 2: Circular Functions and Their Applications

2.1 Unit Circle and Radian Measure

• Definition of Radian: arc length over radius

• Converting Between Degrees and Radians

• Unit Circle Values: exact values for sine and cosine at standard angles (0, π/6, π/4, π/3, π/2, etc.)

• Symmetry and Periodicity on the Unit Circle

2.2 Graphing Circular Functions

• Graphs of Sine, Cosine, and Tangent: domain, range, amplitude, period, axis

• Transformations: vertical shifts, amplitude changes, period changes via horizontal compression/stretch, and phase shifts

• Identifying Graph Features: intercepts, maxima/minima, asymptotes (for tangent), period cycles

2.3 Solving Trigonometric Equations

• Using Unit Circle to Solve: sin(θ) = a, cos(θ) = b, tan(θ) = c

• General Solutions: expressing all solutions using periodicity (e.g. θ = α + 2nπ)

• Solving Equations Graphically: using technology to approximate where algebraic methods fail

2.4 Applications and Modelling

• Modelling Periodic Phenomena: tides, seasonal variation, circular motion

• Phase Shift Interpretation: delay/advance in periodic behaviour

• Solving Problems in Context: interpreting and applying sine/cosine models to real-world scenarios (e.g. Ferris wheels, pendulums)