How do you find the polar equation of $y = 1 + 3 x$ $y=1+3x$ ?

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Answer 1 · 2018-04-22T13:54:33

$r = \frac{1}{sin θ - 3 cos θ}$ $r=1/(sintheta-3costheta)$

The conversion from Rectangular to Polar:
$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

Substitute for $x$ $x$ and $y$ $y$ :
$r sin θ = 1 + 3 (r cos θ)$ $rsintheta=1+3(rcostheta)$

$r sin θ - 3 r cos θ = 1$ $rsintheta-3rcostheta=1$

Factor out the $r$ $r$ :
$r (sin θ - 3 cos θ) = 1$ $r(sintheta-3costheta)=1$

$r = \frac{1}{sin θ - 3 cos θ}$ $r=1/(sintheta-3costheta)$

How do you find the polar equation of y=1+3xy=1+3xy=1+3x?