Question

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

Answer 1

The equation is `7y=x^2`

Explanation:

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`