What is the polar form of $( 3,-27 )$ ?

Question

1438 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-17T05:24:54

$(3sqrt82,- tan^{-1}(9))$

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

$r = sqrt{3^2 + (-27)^2}$

$= 3sqrt82$

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

$x$ is positive while $y$ is negative $=>$ quadrant IV

Then we find the basic angle by taking inverse tangent of $|y/x|$ .

$alpha = tan^{-1}(|{-27}/3|)$

$= tan^{-1}(9)$

The angle that we are looking for would be

$theta = -alpha$

$= -tan^{-1}(9)$

$~~ -1.460$

Therefore, the polar coordinate is $(3sqrt82,- tan^{-1}(9))$

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 ( 3,-27 )( 3,-27 )?