Aperson is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. what is the exact value of the position of the rider after the carousel rotates 5pi/12 radians?

The origin of the coordinate system is the center of the circle. So we have an angle that measures . so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

Finally, the exact value of the position of the rider after the carousel rotates radians is:

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.