I have the following set of equations from which I need to find δ and φ uniquely (i.e without quadrant ambiguity).(adsbygoogle = window.adsbygoogle || []).push({});

In other words I need to have expressions for tan δ and tan φ involving A,B,C and D which are known quantities.

A=1-sin(squared) δ/2 x sin 4φ

B=1+sin(squared) δ/2 x sin 4φ

C= [sin(squared) δ/2].[1+cos 4φ]

D=2-[sin(squared) δ/2].[1+cos 4φ]

From this I find that φ=(1/2) tan (inverse) [(B-A)/2C].

I cannot find a similar expression for δ or δ/2. I can find it as a cos(inverse) function, but the quadrant anomaly remains.

My question is, Is it at all possible to evaluate δ or δ/2 uniquely (without quadrant ambiguity) from the above set of equations? These are expressions I obtained for a birefringence measurement system involving phase δ and direction of birefringence φ which needs to be evaluated unambiguiously.

Will be thankful for any help.

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# Solving this set of trigonometric equations

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