What is the Cartesian equivalent of polar coordinates $(2, pi/6)$ ?

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Answer 1 · 2014-10-02T00:15:14

$(r,theta)->(2,pi/6)$

$(x,y)->(rcos(theta),rsin(theta))$

Substitute in $r$ and $theta$

$(x,y)->(2cos(pi/6),2sin(pi/6))$

Remember back to the unit circle and special triangles.

$pi/6=30^circ$

$cos(pi/6)=sqrt(3)/2$

$sin(pi/6)=1/2$

Substitute in those values.

$(x,y)->(2*sqrt(3)/2,2*1/2)$

$(x,y)->(sqrt(3),1)$

What is the Cartesian equivalent of polar coordinates (2, pi/6)(2, pi/6)?