Support · Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions
Support Examine the properties sin^(- 1)(- x) = - sin^(- 1)x, cos^(- 1)(- x) = π - cos^(- 1)x, tan^(- 1)(- x) = - tan^(- 1)x and cos^(- 1)x + sin^(- 1)x = π/2 using graphing applications and prove them algebraically
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.
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Prerequisite dot points
Determine the formulas d/dx(sinx) = cosx and d/dx(cosx) = - sinx informally by using the graphs of y = sinx and y = cosx and verify with graphing applications
Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Use the chain rule to differentiate functions of the form sinf(x), cosf(x) and tanf(x)
Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Establish the identities tanθ = sinθ/cosθ and cotθ = cosθ/sinθ, identifying the angles to be excluded in each identity
Mathematics Advanced 11–12 – Year 11 · Trigonometric identities and equations Draft mapping
No checked resources on this prerequisite dot point yet.