(20 12? Shandong) As shown in the figure, in the plane rectangular coordinate system xOy, the initial position of the center of the unit circle is (0, 1), and the position of a point P on the circle a

(20 12? Shandong) As shown in the figure, in the plane rectangular coordinate system xOy, the initial position of the center of the unit circle is (0, 1), and the position of a point P on the circle at this time. Solution: Let the center of the circle be O', the tangent point be A (2 2,0), and connect O'P,

Let a ray parallel to the positive direction of the X axis intersect with O', and the intersection point O' is b (3, 1), and let ∠BO'P=θ.

∫⊙O' equation is (x-2)2+(y- 1)2= 1,

According to the parametric equation of a circle, the coordinate of p is (2+cosθ, 1+sinθ).

∵ The initial position of the center of the unit circle is (0, 1), and the circle rolls to the center of (2, 1).

∴∠AO'P=2, you can get θ=3π2-2.

We can get cosθ=cos(3π2-2)=-sin2, sinθ=sin(3π2-2)=-cos2,

Substituting the above formula, the coordinate of p is (2-sin2, 1-cos2).

∴ the coordinate of op is (2-sin2, 1-cos 2).

So, the answer is: (2-sin2, 1-cos 2)