Cut a 45 degree angle "going the other way".
A 45 degree (Acute) angle.
You need a miter saw. It has a back gauge to butt the wood up to, and then the saw has holders to keep it from wobbling. You can set the angle. It may just have notches for 90 degrees and 45, or it may have a protractor on it.
lay out the pattern on a 45" degree angle on .cloth
If I understand the question correctly, the answer is yes. All angles of the same measure will match up with one another.
Cut a 45 degree angle "going the other way".
When you say "crown cut" I think you are referring to a compound angle cut. A compound angle is 2 angles cut at the same time. In crown for instance you put the trim in the saw at a 45 degree angle, and tilt your saw blade at a 45 degree angle as well.
Make a 45 degree cut like you would for an inside corner. This will show the profile of the trim. Use a coping saw to cut down the profile. Angle the cut back a bit so that only the profile edge will meet the adjoining piece of trim.
A 45 degree (Acute) angle.
You need a miter saw. It has a back gauge to butt the wood up to, and then the saw has holders to keep it from wobbling. You can set the angle. It may just have notches for 90 degrees and 45, or it may have a protractor on it.
A 45 degree cut.
Diagonal of a square?
You set the bevel on your saw to a 45 degree angle. Then set the angle on your saw base to the angle of your plumb cut.
It depends on how you want to cut it. If you want to trim it up, I'd suggest going to a salon or instructing someone else to do it. Section the hair, hold it up at a 90 degree angle, slide your finders all the way up to where you want it cut, having your fingers at an 85-90 degree angle (finger tips pointing downward), and cut along your fingers. I'd still suggest having someone do it for you...the results could be horrible doing it yourself.
The same way you cope any other trim. The first piece is full length, square cut on the end and tight against the wall. Cut a 45 degree angle on the end meeting the first piece to expose the profile and cut the end back along that profile with a coping saw. Over cut the angle back so that only the edge of the cut on the face is in contact with the first piece.
A right angle is 90 degrees. That's like cutting straight across. A 45 degree angle is exactly half of that. Cut on the diagonal.
We'll generally use a "miter box" to hold the stock to be cut in a fixed position, and then hold the saw at a fixed angle to the stock. Most miter boxes will allow 90 degree, 60 degree, 45 degree or 30 degree cuts. Some specialized ones allow you to cut at any arbitrary angle to the stock.