SOLUTION: Determine analytically the value of 't' between 0 and π when {{{5sin(t) = 8sin(t+pi/8)}}} Thanks for your help :)

Use  and  with 





We use only the positives since  is positive.



 

Let  and 



 



Divide both sides by cos(t)







Since A is a radical we multiply top and bottom by the conjugate
of the denominator, hoping to eventually rationalize the denominator.



We calculate AB and A²



 


Rationalizing further:













, approximately

Finding the inverse tangent of the absolute value of that gives .9077424765
radians.  But since the tangent is negative, t must be in the 2nd and
4th quadrants.  But yu are only asking for the 2nd quadrant answer, since
the interval given is between 0 and .

To get the second quadrant answer subtract from .



Edwin