To use these equations, the following sign conventions are required:

1) Tensile strains are positive.

2) Shearing strains that decrease the angle between the two lines at the origin are positive.

3) Angles measured counterclockwise from the reference $x$ -axis are positive.

The normal strain ${\epsilon }_n$ acting at an arbitrary orientation $\theta$ is given by the strain transformation equation:

${\epsilon }_n={\epsilon }_x{\cos }^2\theta +{\epsilon }_y{\sin }^2\theta +{\gamma }_{xy}\sin \theta \cos \theta$

The shear strain ${\gamma }_{nt}$ is given by:

${\gamma }_{nt}=-2({\epsilon }_x-{\epsilon }_y) \sin \theta \cos \theta +{\gamma }_{xy} ({\cos }^2\theta -{\sin }^2\theta )$

To solve this problem, substitute specified values for ${\epsilon }_x$, ${\epsilon }_y$, and ${\gamma }_{xy}$ along with the appropriate values for $\theta$ to solve for ${\epsilon }_n$, ${\epsilon }_t$, and ${\gamma }_{nt}$.