How do you convert (-2, -2sqrt{3})into polar coordinates?

1 Answer
May 5, 2018

(4, (4pi)/3) (radians) or (4, 240^@) (degrees)

Explanation:

Rectangular -> Polar: (x, y) -> (r, theta)

  • Find r (radius) using r = sqrt(x^2 + y^2)
  • Find theta by finding the reference angle: tantheta = y/x and use this to find the angle in the correct quadrant

r = sqrt((-2)^2 + (-2sqrt3)^2)

r = sqrt(4+(4*3))

r = sqrt(4+12)

r = sqrt(16)

r = 4

Now we find the value of theta using tantheta = y/x.

tantheta = (-2sqrt3)/-2

tantheta = sqrt3

theta = tan^-1(sqrt3)

theta = (pi)/3 or (4pi)/3

To determine which one it is, we have to look at our coordinate (-2, -2sqrt3). First, let's graph it:
enter image source here

As you can see, it is in the third quadrant. Our theta has to match that quadrant, meaning that theta = (4pi)/3.

From r and theta, we can write our polar coordinate:
(4, (4pi)/3) (radians) or (4, 240^@) (degrees)

Hope this helps!