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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.