July 16th, 2019, 04:58 PM  #1 
Newbie Joined: Jul 2019 From: baguio Posts: 2 Thanks: 0  trig question
how to solve problems like this? pi = Φ  sin(Φ) 
July 16th, 2019, 05:38 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 
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 xaxis. 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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