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Rotating slopes (Posted on 2006-03-21) Difficulty: 3 of 5
Given a line with slope y/x, find a simple formula for the slope of a second line that forms a 45 degree angle with this line (find slopes for both 45 degrees more and 45 degrees less.)
This can be done without trigonometry.

Find a general formula for any angle.
This requires trigonometry.

See The Solution Submitted by Jer    
Rating: 3.2000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution - how do you use it? | Comment 4 of 5 |
(In reply to Solution by Bractals)

You lost me here.  How would you use this formula for, say a 30 degree rotation?
Where does the 30 go?
-------
Let p/q be the slope of the general angle V and y/x the slope
of angle U.
                                   
                                      y     p
                                     --- + ---
               tan(U) + tan(V)        x     q       px + qy
  tan(U+V) = ------------------- = ------------- = ---------
              1 - tan(U)*tan(V)          y   p      qx - py
                                    1 - ---*---
                                         x   q

  Posted by Jer on 2006-03-22 14:25:41
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