What is the polar form of $(2,3)$ ?

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Answer 1 · 2016-03-17T05:28:36

$(sqrt13,tan^{-1}(3/2))$

To write in polar form, you need to know

the distance from the point to the origin
the angle the line passing through it and the origin makes with the positive $x$ axis.

To solve 1. we use Pythagoras Theorem

$r = sqrt{2^2 + 3^2}$

$= sqrt13$

To solve 2. we first find the quadrant that the point lies in.

$x$ is positive and $y$ is positive $=>$ quadrant I

Then we can find the angle by directly taking inverse tangent of $y/x$ . (Note that this is only applicable to quadrant I).

$theta = tan^{-1}(3/2)$

$~~ 0.983$ (in radians)

Therefore, the polar coordinate is $(sqrt13,tan^{-1}(3/2))$

Note that the answer above is not unique. You can add any integer multiples of $2pi$ to $theta$ to get other representations of the same point.

What is the polar form of (2,3)(2,3)?