Finding an Angle Between Tangent Lines

Date: 10/19/2003 at 03:11:33
From: Taryn
Subject: the angle between tangents


How can I find the angle between the tangents to the graphs of y = e^
(x) and y = e^(-x) at the point of intersection?  I drew both graphs
on my calculator, and drew in the tangents.  I know which angle I'm
meant to be finding, but I'm stuck on how to do it.

Date: 10/19/2003 at 05:18:11
From: Doctor Luis
Subject: Re: the angle between tangents

Hi Taryn,

Just to visualize things better, I've plotted the functions
y = e^x and y = e^(-x) along with their tangents at the point
of intersection.

   

I've labeled the angles so we can start talking about their
relationships.

Now, you can find angles A and B using the slopes of the tangent
lines. To find angle C, we use the triangle formed between the lines
and the x-axis. We know its internal angles add up to pi radians,

   A + B' + C' = pi

where B' = pi - B and C' = pi - C are the supplementary angles
to angles B and C, respectively.

Therefore,

  A + (pi - B) + (pi - C) = pi

You can use this equation to solve for the unknown angle C in
terms of the known angles A and B.

I hope this helped! Let us know if you have any more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/