1.A milling machine has a gear that spins, making one complete rotation counter clockwise every 360 milliseconds. The gear has a tooth with a marker in it as shown in the diagram below. There is a sensor 30mm below the center of the gear as viewed from the diagram that measures the height of the marker. The marker is supposed to start the rotation in the position shown on the left gear. Unfortunately the gears are out of sync and now the rotation starts in the position seen in the image at the right below.

The machinist has a table that tells him the height of the marker, but now needs a mathematician to help him. The gear is 15mm in diameter.

(a)Create two equations for the gear. The first models the height of the point in the gear as it was before the gears went out of sync.

(b)The second models the height of the marker in the machine when the gears are out of synchronization.
Create well-labelled graphs for each of these two situations that model the height of the marker on the gear.

(c)The machinist needs to know the height of the marker in the new and old gear positions at the following angles of rotation. Fill in the following table:
Angle of Rotation Old Marker Height New Marker Height
(d)The machinist needs one final piece of information. For maintenance, he needed to rotate the gear 240° to place the marker at a specific height. What height is this, and what rotation(s) on the new gear would provide the same height?

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