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)