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)274 exam-style questions on Edexcel A Level Maths Trigonometric Functions, covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.