Question

I don't understand this and I'm stuck on these two problems can someone please help

Answer 1

17)

as far as I can tell
`\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}`

18)


`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)} \\\\ -----------------------------\\\\`


`\bf \begin{cases} x=4t\implies (x)/(4)=\boxed{t}\\ y=t^2\\ ----------\\ y=\left( \boxed{(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}`