After endless attempts to do this, no success. Quite frustrated down here.
Browsing through numerous sites which give "answer" to this problem nothing works for me.
In the attachment I have drawn a sinewave. I simply want to cut away its negative half (halve?).
In my note book I wrote how to do this because at one time I succeeded to get this done:
1. select object
2. edit path by nodes (F2)
3. select the nodes to cut away with the "Shift" key pressed
4. select "Break path at selected nodes"
But for some mysterious reason this does not work anymore.
What am I doing wrong, or did I forgot writing down an extra step?

You did everything correctly

The node in the middle is already split into two, you only need to pull on it to drag the node that belongs to the lower half away.
Then delete all nodes you do not need

Moini wrote:You did everything correctly

The node in the middle is already split into two, you only need to pull on it to drag the node that belongs to the lower half away.
Then delete all nodes you do not need

All right Moini that's it!!
At last managed to get this done. Although I have gained now some experience with Inkscape,
searching the internet and a lot of tutorials to solve this problem was quite a disappointing journey.
Thanks a lot .

You're welcome!

If I may:

There's still another way to accomplish this (which I find easier):
Draw a horizontal line on top of your sine curve, at the height where you want it to be split.
Select the sine curve and the new line, then do Path -> Cut Path.
Your sine curve will then consist of several separate objects, and you only need to click on those you don't need and hit Del.
(after this, better group the rest, so you can't accidentally move the remaining parts of the curve relative to each other).

Moine, thanks for writing down the latter possibility.
It did work for me when I do the sequence:
1. draw hor. line where I want the split the sine wave
2. select all (Ctrl+A) , or with the shift key pressed select both the line and the sinewave
3. click on Edit path by nodes (F2) the nodes will show up
4. select Path > Cut Path
5. select the nodes one by one and hit the Del key
This works perfect!
The only thing I do not quite understand is your:
(after this, better group the rest, so you can't accidentally move the remaining parts of the curve relative to each other).
But anyway everything works fine this way.

The sine curve may then consist of several objects, depending on where you cut it. So you may have two bumps, and each bump is a single object now, when before they had been connected by a valley.

If you click on a bump, you can move it independently, and away from the other one, so your sine curve's positive bumps will no longer be in the correct position to each other. If you want to avoid accidental moving, group them before you move anything.

Do not know if I have to add this as a new topic but when I apply this procedure to some other
curves like a circle or a rectangular: NOTHING works.
Yes, I get in the end what I want after several 'trial and error' procedures: splitting part of the original curve into the desired ones, but anyway,
I am feeling very insecure reproducing things.
Can somebody point me to a part of the manual (Moini?) I have to work through getting some understanding please?

No problem, AnalogueMan Look into the status line if something like that happens (at the bottom of the window).
Usually, this will give you a helpful hint.

I can't reproduce that it doesn't work with circles or rectangles, though, in Inkscape 0.91 (which is the same version as yours).
In earlier versions (don't ask me which ones), it didn't work, because circles are circles, not paths, and rectangles are rectangles - not paths.
But in 0.91, they are automatically converted to paths before one of those 'Boolean operations' (Intersection, Difference, ....) is applied.

What does it say in your status line?

------------------------

On our website, Brynn and I have compiled a lot of links to all kinds of helpful stuff (use the English version, Dutch is incomplete):
http://inkscape.org/en/learn/

Manuals are linked in the submenu:
https://inkscape.org/en/learn/books/
For beginners, I would suggest this manual (the main manual is quite technical, and very detailed):
https://www.flossmanuals.net/inkscape/

If you can read and understand French as well as English, there is also this (very good) one:
http://www.flossmanualsfr.net/initiation-inkscape/

Inside Inkscape, there are tutorials, too: Help -> Tutorials (again, Dutch may be incomplete - but you can switch the interface language of Inkscape to English via Edit -> Preferences -> Interface: Language, to get access to the English tutorials). These are kind of interactive, too, because they are true SVG documents.

Thanks Moini, I will have a close look at the links you supplied in your latest response.
Will come back to it later but here it is now 22:20 local time (Holland). A little bit late for me to get things going.

The Ellipse and Rectangle tools create a different kind of objects called "shapes". (Also Star and Spiral tools create shapes.) They aren't paths, and don't have nodes, so they can't be edited like paths. But they can be easily converted to paths, using Path menu > Object to Path.

Confusingly, path operations (union, difference, etc.) (including Cut Path) CAN be used directly on shapes, even though they aren't paths. I guess it's just an exception to the rule. But otherwise the shapes need to be converted to path, to edit the nodes.

There are other kinds of objects too. For example, Groups and Clones. With the Selection tool enabled, the status bar will always tell you what kind of object is selected.

However (more confusing info) you can't use Object to Path on Groups or Clones. For clones, you have to break their link to their parent. For Groups, there are a few options. You could Ungroup. Or there's a way to "enter the group" where you can work on individual parts of the.group. But if you use the Node tool, and click on a path that happens to be in a group, you can still work on it with the Node tool, without ungrouping.

When I first started learning Inkscape, I found Help menu > Tutorials to be extremely helpful. Especially I would suggest "Basic", "Shapes", and "Advanced", for beginners. Even though it's called "Advanced" it really covers very basic info. "Elements of Design" and "Tips and Tricks" are also good for general info, but perhaps are somewhat advanced. All the others are for specific techniques (as opposed to general info).

Whoops, you guys both posted while I was typing

Edit
Speaking of manuals, I've always thought this one was good for beginners: http://www.microugly.com/inkscape-quickguide/

Try converting objects to paths (Ctrl+Shift+C). You cannot break down a star/circle/rectangle/text/3Dbox/ so that you preserve them as what they are.

Some notes.
You have a fill with full transparent alpha, probably better switch the fill off?
Speaking of sin waves, you can use the function plotter or the parametric curves extension to render a precise shape -with as many samples as you need and fraction of a phase.
The document and the grid is in mm units, yet the default unit is still px.
Grid snapping is enabled, but not the snapping of the cusp/smooth nodes. The wave is now off the grid.
Switch to outlines only display mode (Ctrl+Shift+5 on the numpad a few times) for a better look.

Moini wrote:what a timing

Exactly.