Problem 37

Step 1.

Note that the curve traced by point on the circumference of the circle as the circle rolls along the straight line known as cycloid.

Take the radius of the circle is .

Now, the parameter for the angle of rotation of the circle is for at the origin.

For the case when circle rotates radians from the angle , this is because when the circle is in contact with the line, then the distance it rolls from the origin is,