Pendulum Motion A wooden bob is suspended from a piece of string of length L to create a pendulum....

Pendulum Motion A wooden bob is suspended from a piece of string of length L to create a pendulum. The accompanying figure shows two orientations of the pendulum (AC and AD) as it rocks from side to side.

Another orientation of the pendulum, AE, shows the position of the bob if the pendulum were completely still and the bob hung vertically. We can draw a horizontal line segment CD that connects the corresponding positions of the bob. Point B is the midpoint of CD. Another vertical line segment, AB, can be drawn to show that AC and AD are mirror images with respect to AB. The angle between the two orientations of the pendulum is ??, and h represents the height of the bob above the vertical position it would assume (point E) if the pendulum hung vertically. (Note: The figure shows what h, the height of the bob, looks like when the bob is in position D.)

(a) Express cos  in terms of L and h.

(b) Express h in terms of cos and L.

(c) Use your answer to part (b) to find the value of h if L = 6, sin ?? is in the first quadrant.