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1.5 Trigonometry

1.5 Trigonometry

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Question 209

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]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

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