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VinnyCee
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Homework Statement
This is part of a larger engineering problem, I have reduced it to this mathematical equation, which should be simple, right?
I need to find when the following EQ has Maximum's (in terms of x):
[tex]\left|4\,cos\left(\frac{2\pi}{5}\,-\,30\,X\right)\,-\,4\,cos\left(\frac{2\pi}{5}\,+\,30\,X\right)\right|[/tex]
Homework Equations
The Attempt at a Solution
I guess take a derivative to find when the maximum and minimums are...
[tex]120\,sin\left(\frac{2\pi}{5}\,-\,30\,X\right)\,+\,120\,sin\left(\frac{2\pi}{5}\,+\,30\,X\right)[/tex]
set that equal to zero and solve for X, so I get the following equation...
[tex]-sin\left(\frac{2\pi}{5}\,-\,30\,X\right)\,=\,sin\left(\frac{2\pi}{5}\,+\,30\,X\right)[/tex]
I can't solve that!
I put it into maple, this is what it gave...
[tex]-\frac{\pi}{300}\,-\frac{1}{30}\,arctan\left[4\,cos\left(\frac{3\pi}{10}\right)\,sin\left(\frac{3\pi}{10}\right)\,+\,2\,cos\left(\frac{3\pi}{10}\right)\right]\,\,=\,\,-0.0524[/tex]The answer is given in the text, but I can't seem to arrive at the same conclusion!
Supposedly, the answer (for the maxima) is...
[tex]X\,=\,\frac{\pi}{60}\,+\,\frac{2\,n\,\pi}{30}[/tex]
and for the minima...
[tex]X\,=\,\frac{n\pi}{30}[/tex]
but when I solve the original EQ (before taking the derivative) by graphing to find the max's - it's 1.1 - 3.3 - 5.5 - etc. which is a factor of 5 off from the book answer just above! not sure how to proceed from here!
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