A robotic welding arm's joint angle $θ\theta$ (in radians) is programmed to follow a path defined by the sensor input $x$ such that

\theta = \frac{2}{3} \arcsin \left( \frac{x-8}{12} \right) + \frac{5\pi}{6}

the valid operating range of the sensor corresponds exactly to the natural domain of the $arcsin⁡\arcsin$ function. Point $R$ is the endpoint of the resulting curve with the maximum joint angle.

Select the correct coordinates of point $R$ from the options below:

\frac{7\pi}{6}) \quad\quad (20, \frac{\pi}{6}) \quad\quad (8, \frac{5\pi}{6}) \quad\quad (12, \frac{7\pi}{6})

A robotic welding arm's joint angle $θ\theta$ (in radians) is programmed to follow a path defined by the sensor input $x$ such that

\theta = \frac{2}{3} \arcsin \left( \frac{x-8}{12} \right) + \frac{5\pi}{6}

the valid operating range of the sensor corresponds exactly to the natural domain of the $arcsin⁡\arcsin$ function. Point $R$ is the endpoint of the resulting curve with the maximum joint angle.

Select the correct coordinates of point $R$ from the options below:

\frac{7\pi}{6}) \quad\quad (20, \frac{\pi}{6}) \quad\quad (8, \frac{5\pi}{6}) \quad\quad (12, \frac{7\pi}{6})

3.5 Trigonometry (A-level only)

Question 33

Markscheme

3.5 Trigonometry (A-level only)

Question 33

Markscheme

3.5 Trigonometry (A-level only)

Question 33

3.5 Trigonometry (A-level only) Questions

3.5 Trigonometry (A-level only)

Question 33

3.5 Trigonometry (A-level only) Questions