Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Let L be the circle in the x-y plane with center the origin and radius 76.
Let S be a moveable circle with radius 68 . S is rolled along the inside of L without slipping while L remains fixed.
A point P is marked on S 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 (8,0) .
After S has moved counterclockwise about the origin through an angle t the position of P is x=8cost+68cos(2/17 t)
y=8sint-68sin(2/17 t)
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).
S makes several complete revolutions about the origin before P returns to (76,0). This is all the information and it is enough to solve the problem.