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Given formula

$asin ( x ) = b sin( x + \phi)$

where $a$ and $b$ are constants. I want to calculate $\phi$.

drhab
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wildcolor
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  • Is $x$ a given number, or do you want this to be an identity which holds for all $x$? – Hans Lundmark Oct 16 '14 at 14:56
  • x is a variable. Please see my comment to Dr. Sonnhard – wildcolor Oct 16 '14 at 16:35
  • In that case, you are asking too much! If $a$ and $b$ are given, there will usually not exist such a number $\phi$. Exceptions occur if $a=b$ (in which case $\phi=0$ will do) and if $a=-b$ (then $\phi=\pi$ works). – Hans Lundmark Oct 16 '14 at 16:56

1 Answers1

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we obtain for $b\ne 0$
$\frac{a}{b}\sin(x)=\sin(x+\phi)$
$\arcsin\left(\frac{a}{b}\sin(x)\right)-x=\phi$

Dr. Sonnhard Graubner
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  • thanks very much for the answer. But according to your solution, the value of the phase shift phi will be depent on the value of x? Actually the real formula I have is this: asin(2pit)+bsin(2pit+phi)=csin(2pi*t) These are actually 3 sinwave signals. By adjusting the phase shift in signal 'b', I will be able to match the sum of signal (a+b) to signal c. So, should phi be independent to variable x? – wildcolor Oct 16 '14 at 16:18