Parametric Curve(s)

$$$ \forall\alpha\in\{0,2\pi\}\quad\; 0.01\leqslant\;k_{a}\;\leqslant0.5\quad\;$$$
$$$ \left \{ \begin{array}{r c l} \theta(\alpha)& = &\alpha \\ r(\alpha)& = &k_{a}\times\left (\sin^{0.4}{(\frac{\alpha}{2})}-\frac{4}{3.5}\right ) \end{array}\right .$$$