Answer: (–34.6, –20)
Step-by-step explanation:
Let the center of the carousel represent the origin on the coordinate plane and Zoe’s position after the 210° rotation have coordinates (x, y ). The definitions of sine and cosine can then be used to find the values of x and y . The value of r is 80 ÷ 2 or 40.
The seat rotates 210o, so the reference angle is 210o – 180o or 30o. Because the final position of the seat corresponds to Quadrant III, the sine and cosine of 210° are negative.
Therefore, the position of her seat relative to the center of the carousel is
(–34.6, – 20).
