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.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
