1. Write a function to describe the position of the tip of the stick not attached to the wheel as the wheel is rolling on a plane, i.e. in terms of the parameter t, the angle of rotation of the wheel. We suggest a step by step approach in (a) - (e) below.

a. In terms of the angle of rotation, what is the horizontal displacement of the point where the stick is attached to the wheel ?

b. In terms of the angle of rotation, what is the vertical displacement of the point where the stick is attached to the wheel?

c. In terms of the angle of rotation, what is the horizontal displacement of the tip of the stick from the point where it is attached to the wheel?

d. In terms of the angle of rotation, what is the horizontal displacement of center of the rolling wheel?

e. What is the total horizontal displacement of the dragging tip of the stick that is not attached to the wheel?