How do you convert (2,23)into polar coordinates?

1 Answer
May 5, 2018

(4,4π3) (radians) or (4,240) (degrees)

Explanation:

Rectangular Polar: (x,y)(r,θ)

  • Find r (radius) using r=x2+y2
  • Find θ by finding the reference angle: tanθ=yx and use this to find the angle in the correct quadrant

r=(2)2+(23)2

r=4+(43)

r=4+12

r=16

r=4

Now we find the value of θ using tanθ=yx.

tanθ=232

tanθ=3

θ=tan1(3)

θ=π3 or 4π3

To determine which one it is, we have to look at our coordinate (2,23). First, let's graph it:
enter image source here

As you can see, it is in the third quadrant. Our θ has to match that quadrant, meaning that θ=4π3.

From r and θ, we can write our polar coordinate:
(4,4π3) (radians) or (4,240) (degrees)

Hope this helps!