17)
as far as I can tell [tex]\bf x=rcos(\theta)\qquad \qquad y=rsin(\theta)\\\\
-----------------------------\\\\
\begin{cases}
x=4cos(\theta)\\
y=4sin(\theta)
\end{cases}\qquad rcos(\theta)=4cos(\theta)\implies r=\cfrac{4cos(\theta)}{cos(\theta)}
\\\\\\
r=\boxed{4}[/tex]
18)
[tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\
-----------------------------\\\\[/tex]
[tex]\bf \begin{cases}
x=4t\implies \frac{x}{4}=\boxed{t}\\
y=t^2\\
----------\\
y=\left( \boxed{\frac{x}{4} }\right)^2
\end{cases}\implies rsin(\theta)=\cfrac{[rcos(\theta)]^2}{4^2}
\\\\\\
rsin(\theta)=\cfrac{r^2cos^2(\theta)}{16}\implies sin(\theta)=\cfrac{rcos^2(\theta)}{16}\implies 16sin(\theta)=rcos^2(\theta)
\\\\\\
\cfrac{16sin(\theta)}{cos^2(\theta)}=r\implies 16\cdot\cfrac{sin(\theta)}{cos(\theta)}\cdot \cfrac{1}{cos(\theta)}=r\implies \boxed{16 tan(\theta)sec(\theta)=r}[/tex]
