How do you convert the rectangular point $(-sqrt3,1)$ into polar form?

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Answer 1 · 2016-11-16T11:33:24

The polar coordinates are $(2,(5pi)/6)$

To convert rectangular coordinates to polar coordinates, we use the following equations

$x=rcostheta$

$y=rsintheta$

$x^2+y^2=r^2$

$(x,y)=(-sqrt3,1)$
Therefore, $r^2=(-sqrt3)^2+1=4$

So, $r=2$

$-sqrt3=2costheta$ and $1=2sintheta$

$costheta=-sqrt3/2$

and $sintheta=1/2$

$theta$ is in the second quadrant, and theta=5pi/6

So, the polar coordinates are $(2,(5pi)/6)$

How do you convert the rectangular point (-sqrt3,1)(-sqrt3,1) into polar form?