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)#