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1 Unit 1: Pure Mathematics A

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Question 416

The angle of rotation ψ\psiψ of a high-precision robotic arm, where 0<ψ<π0 < \psi < \pi0<ψ<π, is determined by the following equilibrium equation:

4cot⁡2ψ+2=4csc⁡ψ+13 4\cot^2 \psi + 2 = 4\csc \psi + 13 4cot2ψ+2=4cscψ+13
a.

Show that the equation can be written in the form

acsc⁡2ψ+bcsc⁡ψ+c=0 a\csc^2 \psi + b\csc \psi + c = 0 acsc2ψ+bcscψ+c=0

where aaa, bbb, and ccc are integers to be found.

[3]
b.

Hence, given that the robotic arm is positioned at an obtuse angle ψ\psiψ that satisfies the original equation, find the exact value of tan⁡ψ\tan \psitanψ. Fully justify your answer.

[4]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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