Example 4: A small windmill has its center \( 6 m \) above the ground and blades \( 2 m \) in length. In a steady wind, a point \( p \) at the tip of one blade makes a complete rotation in \( 12 s \) .
a) If the rotation begins at the highest possible point, sketch a graph of the height of the position \( p \) above the ground at time \( t \) .
b) Write an equation for the function in part a).
c) What is the height of point \( p \) at \( 5 s \) and \( 40 \) s?
d) At what time is \( p \) exactly \( 7 m \) above the ground?