# How do you work out the position of a rotated line?

If I have a line segment that starts at origins and is parallel to the x-axis, how do I work out the position on the X axis of x if it is rotated by say 45 degrees?

I know the degree and I know the length of the line.. so I use what formula?

Is it cos(angle) / length?

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Draw a picture -- it's a right triangle. Then you're pretty much done. –  Jonathan Sep 21 '12 at 4:44
could you explain that.. I need a way to write is in a formula? –  aJynks Sep 21 '12 at 4:52
the hypotenuse is your line segment's length and the angle it makes with the $x$-axis is your angle. The answer will turn out to be $({\rm length})\cdot\cos({\rm angle})$. –  Jonathan Sep 21 '12 at 4:53
so what was that stuff on the wiki en.wikipedia.org/wiki/Rotation_%28mathematics%29#Matrix_algebra ... Like it semaed to say "the new position of x = cos(angle) - sin(angle) * length" –  aJynks Sep 21 '12 at 5:03
I'm not sure where you're finding the thing you're referring to. In your case, you are looking for $x'$ while $x={\rm length}$ and $y=0$. –  Jonathan Sep 21 '12 at 5:16