Answer
$$\frac{3}{16}$$
Work Step by Step
We find:
$\frac{\left|x^{\prime} y^{\prime \prime}-y^{\prime} x^{\prime \prime}\right|}{\left(x^{\prime 2}+y^{\prime 2}\right)^{3 / 2}}=\kappa $
$4 \cos 2 t=x^{\prime}(t) \quad 3 \cos t=y^{\prime}(t)$
$-8 \sin 2 t =x^{\prime \prime}(t) \quad -3 \sin t=y^{\prime \prime}(t)$
$x^{\prime}(\pi / 2)=-4 \quad y^{\prime}(\pi / 2)=0$
$x^{\prime \prime}(\pi / 2)=0 \quad y^{\prime \prime}(\pi / 2)=-3$
$\kappa=\frac{|-4(-3)-(0)(0)|}{(16+0)^{3 / 2}}=\frac{12}{16^{3 / 2}}=$
$\frac{3}{16}$
