ZIMSEC · Form 6 · Upper 6
Further Mathematics
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- Polar coordinates A point is given by (r, θ): x = r cos θ, y = r sin θ, r² = x² + y².
- Further calculus: hyperbolic functions, reduction formulae and applications sinh x = (eˣ − e⁻ˣ)/2; cosh x = (eˣ + e⁻ˣ)/2; tanh x = sinh x/cosh x.
- Complex numbers and de Moivre's theorem (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ, for any integer n (proved by induction for positive n).
- Second-order differential equations Auxiliary equation am² + bm + c = 0: