To convert a rectangular equation (an equation in terms of rectangular, or cartesian coordinates (x,y)), just use the conversion formulas in this video to replace all of the x and y variables with r and theta variables.

You can convert polar coordinates to cartesian coordinates, or vice versa, using the conversion formulas given in this video.

Finding the surface area of the three-dimensional figure that's created by revolving the area under a parametric curve around the x-axis.

You can find the volume of revolution (volume of rotation) of a parametric curve using the formulas from this video.

You'll find the equation of the tangent line to a parametric equation in the same way that you found the tangent line to a regular equation. The only thing that's different is how you take the derivative of a parametric curve versus a regular curve, and that you have to plug a t-value into both x(t) and y(t) to find the coordinate point that represents the point of tangency.

Given two equations, one for x and one for y, both in terms of a third parameter variable t, eliminating the parameter is as simple as solving one of the equations for t and making a substitution into the other equation. This will leave you with one equation instead of two, which will be in terms of x and y only, the parameter variable having been eliminated.

This video shows how to find the equilibrium quantity, equilibrium price, and consumer and producer surplus of a system, given equations for supply and demand.

This is an example of how to find the present value of a continuous income stream (regular deposits) after t years, assuming an interest rate r and that interest is compounded continuously.

This is an example of how to find the future value of a continuous income stream (regular deposits) after t years, assuming an interest rate r and that interest is compounded continuously.

This is an example of how to find the future value of a sum of money after t years, assuming an interest rate r and that interest is compounded continuously.