A robotic arm rotates such that its displacement angle α\alphaα in radians satisfies the drive torque equation:
3sinα(4cot22α−5)=8secα 3 \sin \alpha (4 \cot^2 2\alpha - 5) = 8 \sec \alpha 3sinα(4cot22α−5)=8secαShow that this equation can be expressed in the form
12csc22α−16csc2α−27=0 12 \csc^2 2\alpha - 16 \csc 2\alpha - 27 = 0 12csc22α−16csc2α−27=0Hence, 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.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
