How do you convert $y = x^{2}$ $y=x^2$ into a polar equation?

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How do you convert $y = x^{2}$ $y=x^2$ into a polar equation?

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Answer 1 · 2016-01-20T21:42:48

$r = tan θ sec θ$ $r = tanthetasectheta$

Explanation:

using the links between Cartesian and Polar coordinates.

$∙ x = r cos θ$ $• x = rcostheta$

$∙ y = r sin θ$ $• y = r sintheta$

We can now write the above equation as :

$r sin θ = {(r cos θ)}^{2} = r^{2} {cos}^{2} θ$ $r sintheta = ( r costheta )^2 = r^2 cos^2theta$

(dividing both sides by r )

$\frac{r sin θ}{r} = \frac{r^{2} {cos}^{2} θ}{r}$ $( rsintheta)/r = (r^2cos^2theta)/r$

$sin θ = r {cos}^{2} θ$ $sintheta = rcos^2theta$

$\Rightarrow r = \frac{sin θ}{cos θ} \times \frac{1}{cos θ} = tan θ sec θ$ $rArr r = sintheta/costheta xx 1/costheta = tantheta sectheta$

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How do you convert $y = x^{2}$ $y=x^2$ into a polar equation?

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