Maths Interactives
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Unit 3
· Topic 2
Topic 2: Mathematical induction and trigonometric proofs
Mathematical induction
8 hours
Understand the nature of inductive proof including the use of initial statement, assumption statement, inductive step and conclusion.
2 interactives
Use sigma notation (Σ) to represent a sum.
1 interactive
Prove results for sums for any positive integer n.
Prove divisibility results for any positive integer n.
Prove De Moivre’s theorem for powers of positive integers.
Trigonometric proofs using De Moivre’s theorem
2 hours
Prove multi-angle trigonometric identities up to angles of 4θ by equating parts using the binomial expansion and De Moivre’s theorem, e.g. cos(3θ) = 4 cos³(θ) − 3 cos(θ) and sin(3θ) = 3 sin(θ) − 4 sin³(θ).