Question

A person is on the outer edge of a carousel that is rotating counterclockwise. Using the unit circle to model the carousel, what is the exact position of the riderafter the carousel rotates pi/12 radians

Answer 1

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.

`x=rcos\theta=1cos(\pi)/(12)=(√(6)+√(2))/(4)`

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

`y=rsin\theta=1sin(\pi)/(12)=(√(6)-√(2))/(4)`

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