The angular deflection θ\thetaθ of a precision tracking gimbal is governed by the equilibrium condition
4sinθcosθ2sinθ+3=tanθ,sinθ≠−32 \frac{4 \sin \theta \cos \theta}{2 \sin \theta + 3} = \tan \theta, \quad \sin \theta \neq -\frac{3}{2} 2sinθ+34sinθcosθ=tanθ,sinθ=−23Show that this equation can be written in the form
4sin3θ+2sin2θ−sinθ=0 4\sin^3\theta + 2\sin^2\theta - \sin\theta = 0 4sin3θ+2sin2θ−sinθ=0Determine the possible values for the angular deflection xxx of the gimbal in the range −π2<x<π2-\frac{\pi}{2} < x < \frac{\pi}{2}−2π<x<2π, giving your answers to 3 decimal places where appropriate.
137 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, 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. Each one has a worked solution and a mark scheme showing where the marks go.