By writing cos3ϕ \cos 3\phi\,cos3ϕ as cos(2ϕ+ϕ)\cos(2\phi + \phi)cos(2ϕ+ϕ), show that cos3ϕ=4cos3ϕ−3cosϕ\cos 3\phi = 4\cos^3 \phi - 3\cos \phicos3ϕ=4cos3ϕ−3cosϕ.
Solve, for 0≤ϕ≤1800 \leq \phi \leq 1800≤ϕ≤180, the equation,
12cos3ϕ−9cosϕ=1.5 12\cos^3 \phi - 9\cos \phi = 1.5 12cos3ϕ−9cosϕ=1.5Give your answers to 1 decimal place where necessary.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.