1. Calculus with Parametric Equations
If x = f (t) and y = g(t), then
Ex. Find for the curve given by x = sin t and y = cos t, then find the equation of the line tangent to the curve at

2. Ex. Find all values of t on [0,2π] where the previous curve has a vertical tangent line.

3. Ex. Determine the slope and concavity of the curve given by at the point (2,3)

4. Ex. Set up an integral for the area bounded by the curve and the line y = 2.5.

6. Arc length:

7. Ex. Find the length of the curve given by x = ln t, y = t + 1 for 1 ≤ t ≤ 6

8. Surface Area of Revolution:
This was x or y depending on axis
This will be x(t) or y(t) depending on axis

9. Ex. Set up an integral for the surface area if the curve given by x = , y = t + 2 for 0 ≤ t ≤ 4 is revolved about the x-axis.

10. Pract. For Problems 1-2, consider x = t – sin t, y = 1 – cos t
1. Find the equation of the tangent line where t = .
2. Find the length of the curve for 0 ≤ t ≤ 2π.
3. Show that the surface area of a sphere of radius 1 is S = 4π by parametrizing a semicircle and revolving it.