How do you convert $(theta) = pi/3$ into cartesian form?

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Answer 1 · 2015-11-28T07:58:42

$y = sqrt(3)x$

There are several equalities used to convert between rectangular and polar coordinates. For a list and good explanation as to why they work, see How do you convert rectangular coordinates to polar coordinates?

In this case, as we have no $r$ to consider, we will only need

$y/x = tan(theta)$

Multiplying both sides by $x$ gives

$y = tan(theta)x$

But substituting $theta = pi/3$ we get

$y = tan(pi/3)x$

$=> y = sqrt(3)x$

(Note that this is as expected, as the polar plot $theta = pi/3$ takes on all $r$ values for the angle $pi/3$ , forming a straight line)

How do you convert (theta) = pi/3(theta) = pi/3 into cartesian form?