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.
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.