I have to find the area of this region, but I'm not quite sure what my limits are for it.
Thanks for your help!
r^2=4sin2ø
Plot points until you see it. Watch out for multiple laps and duplicity and crossing over itself.
Please pardon the 2nd grade algebra lesson. It is more confusing than may be realized. It helps to back up to fundamentals and go one tiny step at a time.
I was worried we were going to get two values. This is an excellent warning that we WILL for future values.
So far, we have (0,0)
...or about 1.861
So we jumped rather far from the Origin and spawned two parts of the graph. This is VERY important. If nothing else, it might mean that limits of will cover the whole figure, rather than requiring
This same effort with maybe , , and will show that this is all it takes to trace the ENTIRE curve. A little thought may suggest that continuing will retrace the curve another time, perhaps a little differently, but trace nonetheless. In this case, it seems that the result goes off the Real plane and you do not get a retrace on , but it comes back for another tracing after that.
With a little practice, you WILL get better at it.