How do you find the rectangular equation for $r=7tanthetasectheta$ ?

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Answer 1 · 2016-11-13T11:06:21

The equation is $7y=x^2$

The conversion from polar coordinates $(r,theta)$ to cartesian coordinates $(x,y)$ is done using the following equations

$x=rcostheta$
$y=rsintheta$
$x^2+y^2=r^2$ and $tantheta=y/x$

RHS $=7tanthetasectheta=(7y)/x*1/costheta=7y/x*r/x$

$LHS=RHS$

$r=7yr/x^2$ $=>$ $7y=x^2$

How do you find the rectangular equation for r=7tanthetasecthetar=7tanthetasectheta?