How do you write the equation using rectangular coordinates given #theta=pi/3#?

1 Answer
sky · Shwetank Mauria
Mar 16, 2018

#y=sqrt3x#

Explanation:

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=tanθ#

Multiplying both sides by #x# gives

#y=xtanθ#

Now substituting #θ=π/3# we get

#y=xtan(π/3)#

#=>y=sqrt3x#

Note that this is as expected, as the polar plot #θ=π/3# takes on all
#r# for values for the angle #π/3#, forming a straight line.

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