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1.8 E: Trigonometry

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Question 127

A robotic arm rotates such that its displacement angle α\alphaα in radians satisfies the drive torque equation:

3sin⁡α(4cot⁡22α−5)=8sec⁡α 3 \sin \alpha (4 \cot^2 2\alpha - 5) = 8 \sec \alpha 3sinα(4cot22α−5)=8secα
a.

Show that this equation can be expressed in the form

12csc⁡22α−16csc⁡2α−27=0 12 \csc^2 2\alpha - 16 \csc 2\alpha - 27 = 0 12csc22α−16csc2α−27=0
[4]
b.

Hence, for 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​, determine the possible values of the displacement angle α\alphaα, giving your answers to 3 significant figures.

[5]
Markscheme

1.8 E: Trigonometry Questions

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

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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