To convert rectangular equations into polar equations, we’ll use three conversion formulas: x=rcos(theta), y=rsin(theta), and r^2=x^2+y^2.
Read More
To find the points of intersection of two polar curves, 1) solve both curves for r, 2) set the two curves equal to each other, and 3) solve for theta. Using these steps, we might get more intersection points than actually exist, or fewer intersection points than actually exist. To verify that we’ve found all of the intersection points, and only real intersection points, we graph our curves and visually confirm the intersection points.
Read More
The best way to solve for the area inside both polar curves is to graph both curves, then based on the graphs, look for the easiest areas to calculate and use those to go about finding the area inside both curves. We’ll solve for the points of intersection and use those as the bounds of integration.
Read More
Given a parametric curve where our function is defined by two equations, one for x and one for y, and both of them in terms of a parameter t, like x=f(t) and y=g(t), we can eliminate the parameter value in a few different ways.
Read More