How do you convert $y = \sqrt{3} x$ $y = sqrt(3)x$ into polar form?

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Answer 1 · 2015-12-04T16:54:19

Use these identities ...
$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

Using substitution , insert the identities above into the equation:

$r sin θ = \sqrt{3} \times r cos θ$ $rsintheta=sqrt3xxrcostheta$

$r (sin θ - \sqrt{3} cos θ) = 0$ $r(sintheta -sqrt3costheta)=0$

$sin θ = \sqrt{3} cos θ$ $sintheta=sqrt3costheta$

$tan θ = \sqrt{3}$ $tantheta=sqrt3$

$θ = \frac{π}{3}$ $theta=pi/3$

So, polar form is a straight line : $θ = \frac{π}{3}$ $theta = pi/3$

hope that helped

How do you convert y = sqrt(3)xy=√3xy = sqrt(3)x into polar form?