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

1 Answer
Bio
Mar 19, 2016

(sqrt13,pi-tan^{-1}(3/2))(√13,π−tan−1(32))

Explanation:

To write in polar form, you need to know

  1. the distance from the point to the origin
  2. the angle the line passing through it and the origin makes with the positive xx axis.

To solve 1. we use Pythagoras Theorem

r = sqrt{(-2)^2 + 3^2}r=√(−2)2+32

= sqrt13=√13

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

yy is positive while xx is negative =>⇒ quadrant II

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

alpha = tan^{-1}(|3/{-2}|)α=tan−1(∣∣∣3−2∣∣∣)

= tan^{-1}(3/2)=tan−1(32)

The angle that we are looking for would be

theta = pi-alphaθ=π−α

= pi-tan^{-1}(3/2)=π−tan−1(32)

~~ 2.16≈2.16

Therefore, the polar coordinate is (sqrt13,pi-tan^{-1}(3/2))(√13,π−tan−1(32)).

Note that the answer above is not unique. You can add any integer multiples of 2pi2π to thetaθ to get other representations of the same point.

Related questions
See all questions in Introduction to Polar Coordinates
Impact of this question
1521 views around the world
You can reuse this answer
Creative Commons License