The angular displacement, ϕ\phiϕ, of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:
11secϕ=32sinϕ 11 \sec \phi = 32 \sin \phi 11secϕ=32sinϕShow that this equation can be expressed in the form sin2ϕ=k\sin 2\phi = ksin2ϕ=k, where k k\,k is a constant to be determined.
Hence, find the smallest positive value of ϕ\phiϕ, in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.
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.
