Any advice on how to sketch polar graphs? I have tried transforming to rectangular coordinates, but its not really much help $$ r=1+\sin(\theta) \\ r^2=4\cos(2\theta) $$ Thanks in advance :)
2026-03-30 02:48:01.1774838881
Sketch the polar graphs
323 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The easiest way to sketch polar graphs is to plug in "nice" values of $\theta$ (e.g.,$ \frac{\pi}{4},\frac{\pi}{2},\pi,\frac{3\pi}{2},$ etc.) and plot the points you get to see if you can see the curve.
Plotting these points gives you the rough idea that the graph of the first one is a cardioid. (You can do it yourself or look at about page 6 of http://cims.nyu.edu/~kiryl/Precalculus/Section_8.2-Graphs%20of%20Polar%20Equations/Graphs%20of%20Polar%20Equations.pdf)
You can do the same for the other equation to see that its graph is that of a lemniscate (although for this one you may have to choose your points wisely, because the domain is restricted).
Another method is also to recognize that certain equations correspond to certain graphs.