Question $3(4\mathrm{.}29)$

The displacements for a rigid$-$body rotation through an angle $$ about an axis may be described by

$u(x,y)=(cos-1)x-siny$

$v(x,y)=sinx+(cos-1)y$

Determine the rotation ${}_z$ and the strains; do the strains vanish? What are the values of the strains

and the value of ${}_z$ when the rotation $$ is small?