SOLUTION: The line y=x/2 makes an angle w with the positive x-axis. The line y=mx makes an angle 2w with the positive x-axis. Compute m.

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Question 1114028: The line y=x/2 makes an angle w with the positive x-axis. The line y=mx makes an angle 2w with the positive x-axis. Compute m.
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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The line  y = x/2  has the slope of 0.5.


Hense, the angle w is  such that  tan(w) = 0.5,  i.e.  w = atan(0.5).


Then  tan(2w) = %282%2Atan%28w%29%29%2F%281-tan%5E2%28w%29%29 = %282%2A0.5%29%2F%281-0.5%5E2%29 = 1%2F%281-1%2F4%29 = 1%2F%28%283%2F4%29%29 = 4%2F3.


Thus  m = tan(2w) = 4%2F3.


Answer.  m = 4%2F3.

Solved.