Find polar coordinates of the point whose cartesian coordinates are given. (-2√3 , 2)

Question

Find polar coordinates of the point whose cartesian coordinates are given. (-2√3 , 2)

Answer 1

First let us determine r as follows

r² = x² + y² = 12 + 4 = 16

therefore r = 4

Now we can find θ

x = r cos θ, therefore cos θ = x / r = - √3 / 2

similarly

y = r sin θ, therefore sin θ = y / r = 1 / 2

Positive sin and negative cos indicate that θ is in the second quadrant.

The only angle in the second quadrant with sin θ = 1/2 is θ = π - π/6 = 5π/6

Hence the answer is (4, 5π/6)