A pumpkin pie in a 9.00 in diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate moves through a distance of 233 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.

Given that,

Pie diameter = 9 in

Then, the circumference of the pie is

P = πd = 9π in

Then rim of the pie rotates 233 in,

Then,

1 Revolution of the pie is 9π in,

So, for 233 in, we will have

233 in / 9π in revolution

8.24 revolution

So, the revolution of the pie is 8.24

1 revolution is 2πrad

Then,

8.24 revolution = 8.24 * 2π = 51.78 rad.

And also, 1 revolution is 360°

Then,

8.24 revolution = 8.24 * 360 = 2966.4°

So,

In revolution, θ = 8.24 revolution

In radian = θ = 57.78 rad

In degree θ = 2966.4°