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)+65π\nthe\nthe\nthe 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)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.
