A robotic welding arm's joint angle θ\thetaθ (in radians) is programmed to follow a path defined by the sensor input xxx such that
θ=23arcsin(x−812)+5π6 \theta = \frac{2}{3} \arcsin \left( \frac{x-8}{12} \right) + \frac{5\pi}{6} θ=32arcsin(12x−8)+65πthe valid operating range of the sensor corresponds exactly to the natural domain of the arcsin\arcsinarcsin function. Point RRR is the endpoint of the resulting curve with the maximum joint angle.
Select the correct coordinates of point RRR from the options below:
(20,7π6)(20,π6)(8,5π6)(12,7π6) (20, \frac{7\pi}{6}) \quad\quad (20, \frac{\pi}{6}) \quad\quad (8, \frac{5\pi}{6}) \quad\quad (12, \frac{7\pi}{6}) (20,67π)(20,6π)(8,65π)(12,67π)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.