(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to find the intersection point of y=cos(x*L) and y=x. I need the solution in terms of pi and L and only need the x component of the intersection point. I think the solution will be in the form of x = some_number*pi/L

2. Relevant equations

I know that the L in cos(x*L) just compresses the cosine wave so that instead of the period being 2*pi it is 2*pi/L.

I also know that y=x is simply a 45 degree line.

3. The attempt at a solution

First, I plotted y=cos(x) and y = x and found this intersection point to be 0.235*pi.

Then, I tried to plot y=cos(x*L) but can't seem to find a tool to actually give me this plot because L is a variable.

I know the actual intersection point will depend on L, but that's OK because I need the result in terms of L.

I tried to use x = 0.235*pi/L as the solution but that fails because only the cosine wave is compressed by L, not the y=x line. For example, if L=2, the result is NOT 0.235*pi/2 = 0.1175*pi. Instead it would be 0.1639*pi.

I think I am so close, but can't make the final step.

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# Homework Help: Finding Solution to cos(x*L)=x

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