What are the polar coordinates of $(1, \sqrt{3})$ $(1, sqrt3)$ ?

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What are the polar coordinates of $(1, \sqrt{3})$ $(1, sqrt3)$ ?

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Answer 1 · 2015-11-28T17:33:46

I found: $(2, \frac{π}{3})$ $(2,pi/3)$

Explanation:

Consider the following diagram:

enter image source here
We can see that the relationships between rectangular and polar coordinates are:
$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$θ = arctan (\frac{y}{x})$ $theta=arctan(y/x)$
and:
$x = r cos (θ)$ $x=rcos(theta)$
$y = r sin (θ)$ $y=rsin(theta)$

In your case:
$x = 1$ $x=1$
$y = \sqrt{3}$ $y=sqrt(3)$
use them into:
$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$θ = arctan (\frac{y}{x})$ $theta=arctan(y/x)$
to get:
$r = \sqrt{1 + 3} = \sqrt{4} = 2$ $r=sqrt(1+3)=sqrt(4)=2$
$θ = arctan (\sqrt{3}) = 60^{\circ} = \frac{π}{3} rad$ $theta=arctan(sqrt(3))=60^@=pi/3"rad"$

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What are the polar coordinates of $(1, \sqrt{3})$ $(1, sqrt3)$ ?

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Explanation:

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What are the polar coordinates of $(1, \sqrt{3})$ $(1, sqrt3)$ ?