Determine the rotational coordinate of the following objects for the indicated choices of rotational coordinate system.

(a) The tip of the hour hand of a clock at 4:30 p.m., when zero is at noon on the same day and \(\vartheta\) increases in the clockwise direction.

(b) A faucet after being turned 3/4 of a turn in a clockwise direction, starting from zero and with \(\vartheta\) increasing in the counterclockwise direction.

(c) The object in Figure 11.4 if \(\theta=78.3^{\circ}\), when zero is at \(\theta=0^{\circ}\) and \(\vartheta\) increases in the counterclockwise direction.