We'll start out with something that seems reasonable, like 0 ≤ θ ≤ π, and see what we find. PICTURE: graph for 0 ≤ θ ≤ π That's definitely not right. We didn't find all of the petal we wanted, and we got a bunch of other junk. See if we can decrease the upper bound on θ until we find the top half of the petal we want. How about 0 ≤ θ ≤ \frac{π}{2} ? PICTURE: graph for 0 ≤ θ ≤ \frac{π}{2} Still not right. We have the upper half of the petal, but we also have half a petal that we don't want: PICTURE polar funcs 29 This seems like we have twice as much graph as we want, we'll try cutting the upper bound of θ in half again. If 0 ≤ θ ≤ \frac{π}{4} we find PICTURE : graph it That's the upper half of the petal we want. To find the lower half of the petal, let the lower bound for θ reflect its upper bound. When -\frac{π}{4} ≤ θ ≤ \frac{π}{4} we find the piece of the graph we want: PICTURE: graph it |