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/
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