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1 Unit 1: Pure Mathematics A

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Question 88

The angular deflection θ\thetaθ of a precision tracking gimbal is governed by the equilibrium condition

4sin⁡θcos⁡θ2sin⁡θ+3=tan⁡θ,sin⁡θ≠−32 \frac{4 \sin \theta \cos \theta}{2 \sin \theta + 3} = \tan \theta, \quad \sin \theta \neq -\frac{3}{2} 2sinθ+34sinθcosθ​=tanθ,sinθ=−23​
a.

Show that this equation can be written in the form

4sin⁡3θ+2sin⁡2θ−sin⁡θ=0 4\sin^3\theta + 2\sin^2\theta - \sin\theta = 0 4sin3θ+2sin2θ−sinθ=0
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b.

Determine 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.

[5]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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  3. /1 Unit 1: Pure Mathematics A

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