$\"\"$

Let the center of the carousel represent the origin on the coordinate plane and Zoe $\"\"$ s position after the $\"\"$ rotation have the coordinates $\"\"$ .

The definitions of sine and cosine functions are used to find the values of $\"\"$ and $\"\"$ .

The value of $\"\"$ is $\"\"$ .

The seat rotates $\"\"$ , so the reference angle is $\"\"$ .

Because the final position of the seat corresponds to Quadrant III, the sine and cosine of $\"\"$ are negative.

$\"\"$

Find the $\"\"$ -coordinate by using cosine function.

$\"\"$

Find the $\"\"$ -coordinate by using sine function.

$\"\"$

Therefore, the position of joe seat relative to the center of the carousel is $\"\"$ .

$\"\"$

Tthe position of joe seat relative to the center of the carousel is $\"\"$ .