On a sheet of graph paper, plot the points $(x,y)$ in your chart. You should see a smooth curve, otherwise something is off.

Find the vertical position of the speck, $y,$ in terms of $.$

$y()=$

In the diagram it shows that length $"b"$ is below the center but this won't always be the case. For what angles of $$ is $"$b$"$ above the center and how does your function in Question $9$ account for this switch?

Graph this function on a reasonable domain.

Does this function increase, decrease, stay constant or a combination of the above? Why does your answer make sense in context of the problem?

Evaluate and interpret the maximum value on this graph in context

Find the lateral position of the speck, x $,$ in terms of $.$

$x()=$

In the diagram, length $"$a$"$ is behind the center but this won't always be the case. For what angles of $$ is $"a"$ in front of the center and how does your function in Question $3$ account for this switch.

Graph this function on a reasonable domain.

Evaluate and interpret the $y-$intercept in context.

Explain why there is no x$-$intercept in context.

Does this function increase, decrease, stay constant or a combination of the above? Why does your answer make sense in context of the problem?

How to Check That you are in the Ballpark: Plot $(x,y)$ in parametric mode. Is this a smooth$-$flowing curve? If not, make corrections.