How do you write the polar coordinates for the point with rectangular coordinates (0, 3)?

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Answer 1 · 2015-11-06T04:28:03

#(3,90^\circ)#

Polar coordinates are in the form #(r,theta)#

First we need to find the vector, it goes from the origin #(0,0)# to your point #(0,3)#.

#\vec{u}=<0\hat{i}+3\hat{j}> - <0\hat{i}+0\hat{j}> = 0\hat{i} + 3\hat{j}=3\hat{j}#

You can see the vector goes straight up, just in the #y# direction, so the angle is #90^\circ# and the radius #r# is 3. Let's prove that.

As we said, your vector #\vec{u}=3\hat{j}#. Let's find the modulus (radius) of the vector:

#r=|\vec{u}|=\sqrt{3^2}=3#

And the angle will be:

#theta =arctan(3/0)=90^\circ#