grapher
I've graphed two polar curves and would like to shade the region inside one and outside the other. When I select the two equations and then select Integrate from the Equation menu, I get the error message
Cannot integrate the difference between the selected graphs.
It seems simple. Why can't Grapher do it?
In case it makes a difference, the two equations are r = 6 (a circle) and r = 6 - 6 sin(theta) (a cardioid). I want to shade the region inside the cardioid but outside the circle.
It appears as though it's impossible to actually label them in 3D view. Although this probably wasn't the answer you were looking for, there is a workaround.
The reason you can't actually label the graphs:
Labels can not easily be added to 3D graphs because the text would have to be rotated through three dimensions with the graph itself (Apple explained this as difficult to write the code for).
So, a workaround for this:
- Save as a pdf
- Open the graph and then copy it.
- Paste into a word document
- Add any text where you need it with text boxes, label axis.
If you'd like to see the original copy of the above information, you can find it here.
First select both equations in the sidebar, and then Equation » Integration… in the menu.
In the dialog, it has preselected Area Between Curves. Confirm it.
You can change the color in the inspector window.
Since your second equation is y=0, you could just select the first one, and integrate it, selecting Area in the dialog. The result should look the same.
Best Answer
Grapher can do it. Using the conjunction
r > 6 & r < 6 - 6 sin (theta), we get the following