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1.8 E: Trigonometry

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Question 148

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
[5]
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]

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

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.

Question bank