An object moves around a circle of radius 6.2 meters, making a revolution every 7.8 seconds. Assume that its angular velocity is constant. Starting at t = 0, when its angular position is 0 radians, what are the x and y coordinates of its position after t seconds (express your answer in terms of the parameter t)?
Moving through a revolution, which is 2 `pi radians, in 5 seconds, the object will have an angular velocity of
`omega = 2 `pi radians/( 7.8 seconds) = .8055 radians/second.
After t seconds, starting at 0 radians when t = 0, the angular position will be
theta = ( .8055 radians/second ) (t seconds) = .8055 * t radians.
Its x and y coordinates are therefore
x1 = 6.2 meters * cos ( .8055 t)
and
"y = 6.2 meters * sin( .8055 t).