Let L be the circle in the xy plane with center the origin and radius 76. Let S be a moveable circle with radius 64 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on 8 before S is rolled and the path of P is studied. The initial position of P is (76,0). The initial position of the center of S is (12,0) . After 8 has moved counterclockwise about the origin through an angle t the position of P is 3 =12 4 r a: cost+6 cos(16t) 3 = 12 ' 4 ' y smt 6 sm(16t) How far does P move before it returns to its initial position? Hint: You may use the formulas for cos( u+v) and sin( w /2). 8 makes several complete revolutions about the origin before P returns to (76,0)