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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.