Question

convert to rectangular r=4sin theta sec^2 theta

Answer 1

\(\bf r=4sin(\theta)sec^2(\theta)\implies r=4sin(\theta)\cfrac{1}{cos^2(\theta)}\implies r=\cfrac{4sin(\theta)}{cos^2(\theta)}\\ \quad \\
rcos^2(\theta)=4sin(\theta)
\quad \textit{multiply both sides by "r", see what you get}\)

Answer 2

\[r ^{2}\cos ^{2}\theta=4y\]
Now what? I'm lost..

Answer 3

hmm yes so \(\bf r=4sin(\theta)sec^2(\theta)\implies r=4sin(\theta)\cfrac{1}{cos^2(\theta)}\implies r=\cfrac{4sin(\theta)}{cos^2(\theta)}\\ \quad \\
rcos^2(\theta)=4sin(\theta)
\quad \textit{multiply both sides by "r"}\\ \quad \\
r^2cos^2(\theta)=4rsin(\theta)\implies [rcos(\theta)]^2=4y\implies x^2=4y\)

Answer 4

Oh! Okay. When stuff gets squared like THAT it really confuses me.. Thank you :)

Answer 5

yw