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Support · Mathematics Extension 1 11–12 – Year 12 · Further calculus skills

Support Examine the proofs of the derivatives of sin^(- 1)⁡x, cos^(- 1)⁡x and tan^(- 1)⁡x

Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.

Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.

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Prerequisite dot points

Determine the formulas d/dx(sin⁡x) = cos⁡x and d/dx(cos⁡x) = - sin⁡x informally by using the graphs of y = sin⁡x and y = cos⁡x and verify with graphing applications

Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping

  • Interactive toolStarterEnrichment
    Desmos Graphing Calculator
    Desmos · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
  • Interactive toolEnrichment
    GeoGebra Classic
    GeoGebra · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Dynamic geometry and graphing for constructions and proofs.

Use the chain rule to differentiate functions of the form sin⁡f(x), cos⁡f(x) and tan⁡f(x)

Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping

No checked resources on this prerequisite dot point yet.

Model and solve problems involving periodic phenomena using transformations of the trigonometric functions f(x) = sin⁡x, f(x) = cos⁡x or f(x) = tan⁡x, without the use of calculus

Mathematics Advanced 11–12 – Year 12 · Further graph transformations and modelling Draft mapping

No checked resources on this prerequisite dot point yet.