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.

2. To get the y-coordinate, get r sin θ.

Hence, the exact location of the rider after the carousel rotates π/12 radians is given by the coordinates found in Option D.