An object moves at constant angular velocity around a circle of radius 8.5 meters, making a revolution every 8.5 seconds.
After (1/12)( 8.5) seconds, starting at 0 radians when t = 0, the angular position will be 1/12 of a complete circle, or `theta1 = (1/12)(2 `pi ) radians = `pi /6 radians.
This is a familiar angle, 30 degrees above the x axis, with sine equal to 1/2 and cosine equal to `sqrt(3) / 2. On a circle of radius 8.5 meters, the x and y coordinates will therefore be
x1 = 8.5 meters (`sqrt(3) / 2) = 7.361 meters
and
y1 = 8.5 meters (1/2) = 4.25 meters.
After (5/8)( 8.5 seconds), the angular position will be
`theta1 = (5/8)(2 `pi radians) = 5 `pi /4 radians.
This is a third-quadrant angle at 45 degrees from the x axis, with both sine and cosine equal to -`sqrt(2) / 2. On a circle of radius 8.5 meters, the x and y coordinates will therefore be
x2 = 8.5 meters (-`sqrt(2) / 2) = -6.011 meters
and
"y2 = 8.5 meters (-`sqrt(2) / 2) = -6.011 meters.