The physical stress state at a point does not change when the coordinate axes are rotated, but its normal and shear components do.

For a plane-stress state described by $\sigma_x$, $\sigma_y$ and $\tau_{xy}$, the components on a plane rotated by angle $\theta$ can be calculated with stress-transformation equations.

One state, different components

A bar in uniaxial tension can have only normal stress on a plane perpendicular to its axis, yet the same point has both normal and shear components when viewed on an inclined plane.

Rotating the coordinate system does not create a new physical state. It resolves the same internal loading onto differently oriented surfaces.

Why transformation matters

Materials can respond differently to normal and shear loading. Finding the stresses acting on differently oriented planes lets us identify principal stresses, maximum shear stress and the quantities used by later failure criteria.

The trigonometric stress-transformation equations can be evaluated directly or represented graphically using Mohr's circle.