Thursday, July 10, 2014

Largest Triangle Between Sine and Cosine

I saw an interesting question posted online. The author wanted to know what the largest triangle that would fit between a graph of y = sin(x) and y = cos(x) would be.

What's the largest triangle that will fit between the blue and green lines?
I haven't been able to come up with an exact solution using geometry or algebra; if you can do it, I'd like to hear how. Instead I made a tool in excel which animates the process of finding an approximation of the solution by exhaustion:

The program searches through all the different triangles to find the largest
If you'd like to have a peek at which triangle is the biggest you can download the excel file here.

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