A point is moving along a cosine curve . When it is at , its x-coordinate is changing at 3.0 cm/sec. Find the rate of change of the y-coordinate.

From the graph, we see that when the rate of change of the x-coordinate is positive (the point is moving to the right), the y-coordinate is getting smaller (the point is moving downward). Hence, we expect to be negative when is positive and vice versa on this part of the curve.

From the equation of the curve, we have (using the Chain Rule )

.

At the specified position, we have