To determine the location of the rider, we need to convert the polar coordinate to rectangular form.
The given polar coordinate is (1, π/12).
To convert, here are the steps.
1. To get the x-coordinate, get r cos θ.
[tex]x=rcos\theta=1cos\frac{\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]2. To get the y-coordinate, get r sin θ.
[tex]y=rsin\theta=1sin\frac{\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]Hence, the exact location of the rider after the carousel rotates π/12 radians is given by the coordinates found in Option D.