Quick Recap — Trigonometry (Hard)

Chain the tools: amplitude a2+b2\sqrt{a^2+b^2} for asin⁡θ+bcos⁡θa\sin\theta+b\cos\theta, squaring relations like sin⁡θ+cos⁡θ=k\sin\theta+\cos\theta=k, counting solutions of trig equations on an interval, and the cosine rule. Many are numerical-value (Section B), with cross-topic links to complex numbers (De Moivre).