At t = 0 seconds the angular position of an object is 0 radians, and it moves at constant angular velocity around a circle of radius 3.2 meters, making a revolution every 5.8 seconds. What are the x and y coordinates of its position at t seconds?
Moving through a revolution, which is 2 `pi radians, in 5 seconds, the object will have an angular velocity of
`omega = 2 `pi radians/( 5.8 seconds) = 1.083 radians/second.
After t seconds, starting at 0 radians when t = 0, the angular position will be
theta = ( 1.083 radians/second ) (t seconds) = 1.083 * t radians.
Its x and y coordinates are therefore
x1 = 3.2 meters * cos ( 1.083 t)
and
"y = 3.2 meters * sin( 1.083 t).