Substituting principal stress angle into the plane stress transformation equations

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When one substitutes the angle -23.7 into the plane stress transformation equation for SigmaX' you indeed get -46.42 MPa (as shown in the images). However, if you substitute this same angle into the plane stress transformation equation for SigmaY', you yield the other principal stress of 116.4 MPa. My question is how can you conclude the angle -23.7 corresponds to SigmaX' rather than SigmaY' ?
 

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When one substitutes the angle -23.7 into the plane stress transformation equation for SigmaX' you indeed get -46.42 MPa (as shown in the images). However, if you substitute this same angle into the plane stress transformation equation for SigmaY', you yield the other principal stress of 116.4 MPa. My question is how can you conclude the angle -23.7 corresponds to SigmaX' rather than SigmaY' ?
The angle θ is the angle that you have to rotate the x axis to get the x' axis.

Chet
 
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what the difference between angles of theta p and theta which it used to find sigma theta?
 

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