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1 Unit 1: Pure Mathematics A

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Question 84
i.

In a study of harmonic oscillators, a phase angle ϕ\phiϕ is found to satisfy the equation

4cosec⁡ϕ=9cos⁡ϕ 4 \operatorname{cosec} \phi = 9 \cos \phi 4cosecϕ=9cosϕ

for 0<ϕ<π0 < \phi < \pi0<ϕ<π. Determine the possible values of ϕ\phiϕ, in radians, giving your answers to 3 significant figures.

[4]
ii.

The configuration of a robotic linkage is governed by the equation

tan⁡3θ−tan⁡20∘1+tan⁡3θtan⁡20∘=2 \frac{\tan 3\theta - \tan 20^\circ}{1 + \tan 3\theta \tan 20^\circ} = 2 1+tan3θtan20∘tan3θ−tan20∘​=2

for 0∘<θ<180∘0^\circ < \theta < 180^\circ0∘<θ<180∘. Solve this equation to find the possible orientations θ\thetaθ, giving your answers to one decimal place.

[5]
Markscheme

1 Unit 1: Pure Mathematics A Questions

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

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