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)