# Solving this set of trigonometric equations

1. Aug 18, 2015

### Kallol

I have the following set of equations from which I need to find δ and φ uniquely (i.e without quadrant ambiguity).
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.

2. Aug 18, 2015

### fireflies

What is quadratic ambiguity?

Did you try D/C?

3. Aug 19, 2015

### Kallol

I mean quadrant ambiguity, i,e., if we have an expression of the form tan x =a/b, the signs of a and b determine
in which of the 4 quadrants the x lie.

4. Aug 19, 2015

### fireflies

You need not use quadrant ambiguity, you can do it by simple substitutions, and using trigonometric equations

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook