Today in class, we learned about how to find the slope of a tangent line to a curve in Polar. Since slope is defined as change in y over change in x, we need to know r and theta in terms of x and y. So we use x = rcos(theta) and y = rsin(theta). We differentiate each with respect to theta and then divide dy/d(theta) by dx/d(theta), similar to what we did in parametrics, because that will give us dy/dx so that we can plug in theta and find the slope of the line tangent at that point. We can also find the points where there are horizontal tangent lines and the slope of the tangent line at the pole for that graph. It can be quite tedious with a LOT of trig. Hope this helps!
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