Support · Mathematics Extension 2 11–12 – Year 12 · Introduction to complex numbers
Support Prove that (cosθ + isinθ)ⁿ = cosnθ + isinnθ for negative integers n
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
Prove and use the identities sin²nx = 1/2(1 - cos2nx) and cos²nx = 1/2(1 + cos2nx) to find integrals involving ∫sin²nx dx and ∫cos²nx dx
Mathematics Extension 1 11–12 – Year 12 · Further calculus skills Draft mapping
No checked resources on this prerequisite dot point yet.
Use 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 to solve problems, simplify expressions and prove results
Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions Draft mapping
No checked resources on this prerequisite dot point yet.
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
Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions 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.