How do you express the Cartesian coordinates $(sqrt(3)/2, 1/2)$ as polar coordinates?

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Answer 1 · 2016-11-17T12:34:48

The polar coordinate are $=(1,pi/6)$

To convert from cartesian coordinares $(x,y)$ to polar coordinates $(r,theta)$ , we use

$x=rcostheta$

$y=rsintheta$

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

Here, $(x,y)=(sqrt3/2,1/2)$

Therefore, $r^2=3/4+1/4=1$

$r=1$

And, $costheta=x/r=sqrt3/2$

and $sintheta=y/r=1/2$

So , we are in the first quadrant and $theta=pi/6$

The polar coordinates are $(1,pi/6)$

How do you express the Cartesian coordinates (sqrt(3)/2, 1/2)(sqrt(3)/2, 1/2) as polar coordinates?