How do you convert $r sin (θ) = ln (r) + ln [cos (θ)]$ $rsin(theta)=ln(r)+ln[cos(theta)]$ into cartesian form?

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Answer 1 · 2017-02-14T02:52:16

$y = ln x, x > 0$ $y=ln x, x >0$ .

The conversion formula is

$r (cos θ, sin θ) = (x, y)$ $r(costheta, sintheta)=(x, y)$ .

Here,

$y = ln r = ln (\frac{x}{r}) = ln (r (\frac{x}{r})) = ln x$ $y=lnr=ln(x/r)=ln(r(x/r))=lnx$ .

How do you convert rsin(theta)=ln(r)+ln[cos(theta)]rsin(θ)=ln(r)+ln[cos(θ)]rsin(theta)=ln(r)+ln[cos(theta)] into cartesian form?