Skip to content

Course home

1.7.22 Proofs involving trigonometric functions (A-level only)

1.7.22 Proofs involving trigonometric functions (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930
Question 30

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

1.7.22 Proofs involving trigonometric functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.7.22 Proofs involving trigonometric functions (A-level only)

38 exam-style questions on OCR (MEI) A Level Maths 1.7.22 Proofs involving trigonometric functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank