What are the polar coordinates of ##(1, sqrt3)##?

I found: ##(2,pi/3)##

Consider the following diagram:

We can see that the relationships between rectangular and are: ##r=sqrt(x^2+y^2)## ##theta=arctan(y/x)## and: ##x=rcos(theta)## ##y=rsin(theta)##

In your case: ##x=1## ##y=sqrt(3)## use them into: ##r=sqrt(x^2+y^2)## ##theta=arctan(y/x)## to get: ##r=sqrt(1+3)=sqrt(4)=2## ##theta=arctan(sqrt(3))=60^@=pi/3"rad"##