A Unit Plan for Teaching Trigonometric Functions (TAS, TASC-Aligned)

Trigonometric functions are where many senior students either fall in love with mathematics or quietly give up, and the difference often comes down to sequencing. Rush from right-angled triangles to graphs of sine and cosine and students lose the thread; build the arc carefully and the topic becomes one of the most rewarding you teach. This unit plan lays out a sequenced progression of around nine to eleven lessons for a Tasmanian Years 10 to 12 Mathematics class, working within the Australian Curriculum as delivered in Tasmania and preparing students for the reasoning and modelling expected towards the TCE.

The learning arc

The unit moves through four phases: ratio, circle, graph, model. Students begin with trigonometric ratios in right-angled triangles, extend to the unit circle, translate that into the sine and cosine graphs, then apply the functions to model real periodic phenomena. A resource focused on the functions themselves, Trigonometric Functions – Sine and Cosine, maps closely to this arc and supplies the graphing tasks and worked examples that anchor the middle phases.

Lessons 1 to 3: Ratio

Start where students have footing. Trigonometric ratios build directly on right-angled triangle work, so open by connecting to prior knowledge. If the class is shaky on the underlying geometry, a short revision using The Pythagorean Theorem – Applications steadies the foundation before you introduce sine, cosine and tangent as ratios.

1. Lesson 1: Recall right-angled triangles; introduce the three ratios with a physical measuring activity.
2. Lesson 2: Solve for unknown sides and angles in context, such as the height of a Hobart building from its shadow.
3. Lesson 3: Consolidate with mixed problems and a short formative check.

Lessons 4 to 6: Circle and graph

Now make the leap that unlocks the functions. Introduce the unit circle and show how the y-coordinate traces the sine curve as the angle turns. This is the conceptual heart of the unit and the moment to slow down. Use technology so students see the graph generated live from the circle. Building the Critical and Creative Thinking capability here, through genuine sense-making rather than memorisation, pays off across the whole senior course.

Lessons 7 to 9: Model

Trigonometric functions truly matter because they describe things that repeat. Move students into modelling:

• Model the tides in a Tasmanian coastal town over a day.
• Describe the height of a point on a Ferris wheel against time.
• Represent daylight hours across the year, a vivid context given Tasmania's seasonal swing.
• Interpret amplitude, period and phase shift in each real context.

These tasks develop the Numeracy capability and the modelling fluency the TCE rewards. Weaving in proportional reasoning from earlier topics, for example through a quick link to Percentages and Interest – Everyday Mathematics, keeps number sense sharp while the new content is demanding.

Where assessment fits

Assessment should track the arc rather than test only the final skill:

1. Formative (Lesson 3 and Lesson 6): a ratio-solving check, then a graph-interpretation check, each with feedback before the next phase.
2. Summative (Lesson 10 to 11): a modelling task using sine or cosine to describe a real periodic situation, assessed against reasoning and application criteria.

Aligning the summative task to the modelling students have practised makes the unit honest and TASC-ready. Students are judged on the thinking they have genuinely rehearsed, they see trigonometry as a language for the rhythms of the real world, and they leave Tasmanian senior Mathematics with functions they understand rather than formulas they fear.

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