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?

Assuming the riders starts at the position (20, 0) on the x-axis, the exact position of the rider will be (20cos75, 20sin75) or about (5.18, 19.32).

The angle for 5pi/12 radians is 75 degrees. Therefore, to find the position we can use the sine and cosine of 75 to find the x and y value of the coordinate.

For the y-value, we can write and solve:
sin75 = x/20

For the x-value, we can write and solve:
cos75 = x/20

The complex number is given as: 2-8i

So for conjugate, you just flip the sign of the imaginary part:

2+8i will be the answer