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July 16th, 2019, 04:58 PM   #1
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trig question

how to solve problems like this?

pi = Φ - sin(Φ)

mcguriy03 is offline  
 
July 16th, 2019, 05:38 PM   #2
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In this case, it helps to simplify a little bit.
$\displaystyle \Phi - \pi = \sin(\Phi)$
Phase shift identity $\displaystyle \sin(\phi-\pi) = -\sin(\phi)$
Let $\displaystyle x = \Phi - \pi$, then
$\displaystyle x = -\sin(x)$
Plot y = x and y = -\sin(x), and you can easily convince yourself they only intersect at x = 0 $\displaystyle \rightarrow \Phi = \pi$

I would consider that the "smart way," but it requires some thinking and an "aha" moment. If you can't find your "aha" moment, try putting the equation in the form f(x) = 0, plot f(x), and see where it crosses the x-axis. This will give you an approximate answer, and maybe some clues as to how to find the exact answer(s).

Last edited by skipjack; July 17th, 2019 at 10:57 AM.
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