Course: Year 12 Mathematics Advanced

Trigonometric Functions and Graphs

A structured pathway through radians, exact trigonometric values, unit-circle reasoning, and the key features of sine, cosine, and tangent graphs.

Active lessons

7

Planned lessons

7

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Start with radians and exact values before graph work.
  • Use the mastery quiz to check whether key values are secure.
  • If you miss the pass mark, work through the full staged lesson.
  • Return to unit-circle signs when graph or equation questions feel uncertain.

What this unit covers

Radians and degree conversion
Exact trigonometric values
The unit circle
Quadrant signs
Graphs of sine and cosine
The tangent graph and asymptotes
Amplitude, period, and shifts
Trigonometric equations
Identities and simplification
Periodic modelling

Unit pathway

Lesson pathway

7 of 7 active

1

Lesson 1

Radians, exact values, and the unit circle

Convert between degrees and radians, use exact values, and interpret sine, cosine, and tangent on the unit circle.

Active
2

Lesson 2

Graphs of sine, cosine, and tangent

Identify the periods, ranges, intercepts, and asymptotes of the basic trigonometric graphs.

Active
3

Lesson 3

Amplitude, Period, Phase Shift, and Vertical Shift

Describe and sketch transformed trigonometric graphs using amplitude, period, phase shift, and vertical shift.

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4

Lesson 4

Trigonometric Equations

Solve trigonometric equations over specified domains using exact values, graphs, and symmetry.

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5

Lesson 5

Trigonometric Identities and Simplification

Use fundamental trigonometric identities to simplify expressions and support equation solving.

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6

Lesson 6

Modelling Periodic Phenomena

Use trigonometric functions to model periodic contexts such as tides, daylight, height, and motion.

Active
7

Part of the Online Learning Package

This unit is part of the Nova Maths online learning package. The lesson pathway is available for preview, and full access requires an active online learning subscription.

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