The butterfly curve is given by the following parametic equations:

$x=sin(t)(e^{cost}-2cos4t-si{n}^5\frac{t}{12})$

$y=cos(t)(e^{cost}-2cos4t-si{n}^5\frac{t}{12})$

Generate values of $x$ and $y$ for values of $t$ from $0$ to $100$ with $t=\frac{1}{8}.$ Construct plots of:

a$)x$ and $y$ versus $t,$ and

b$)y$ versus $x$

Include titles and axis labels on both plots and a legend for $($a$).$ For $($a$),$ employ a dotted line for $y$ in order to distinguish it from $x.$