Thread: complicated geometry in mechanics

I have to determine the distance along the Z-axis from O to where the upper line crosses the Z-axis and makes angle between the Z-axis and the line.
The lower line which length equals L starts at the origin and makes an angle between the Z-axis and the line itself (so the angle between the line and the X-axis is )


This distance along the Z-axis equals (Lcos + Lsin cotan )ez
ez is the unit vector and there should be an arrow above the letter e.
I don't understand why you can express this distance like this.



Because I'm not certain if the rest of you can see this picture, since it's posted on a secured website (login), I have posted the same picture as an attachment.

Hi

See drawing attached







Therefore

ImageShack - Image Hosting :: drawingue6.jpg

Great, I understand it.

Originally Posted by running-gag

Hi

See drawing attached

This part I understood.

Therefore

This was my problem because I was confused about that cotan, I tried to solve it by using the geometric circle.

OK

Cotangent is only the inverse of tangent



List of trigonometric identities - Wikipedia, the free encyclopedia

That wasn't the problem.
I'll attach another file so you can see which figure I used, then you might understand my confusion.
It's a words-file but it just contains 1 picture (copied from a PDF-file).
I assume you can open this file, otherwise just let me know and I'll try to use Imageschack.
As you can see an arbitrary line which makes an arbitrary angle crosses Y=1 (cartesian graph with X-axis and Y-axis, unit circle with a diameter of 1) at X=cotan angle.