The angular displacement, ϕ\phiϕ, of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:
11secϕ=32sinϕ11 \sec \phi = 32 \sin \phi11secϕ=32sinϕ
Show 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 Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions, matched to the Edexcel A Level Maths (9MA0) 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.