Find the polar co-ordinates of points whose Cartesian co-ordinates are

1.	Find the polar co-ordinates of points whose Cartesian co-ordinates are: (-√3,1)
Answer» (x, y) = (- √ 3, 1) ∴ r = \(\sqrt{x^2+y^2} = \sqrt{3+1}=\sqrt4=2\) tan θ = \(\frac{y}{x} = \frac {1}{-\sqrt3}=-tan \frac{\pi}{6}\) Since the given point lies in the 2nd quadrant, tan θ = tan (π-π/6) …[∵ tan (π – x) = – tan x] ∴ tan θ = tan (5π/6) ∴ θ = (5π/6)= 150° ∴ the required polar co-ordinates are (2, 150°)

Find the polar co-ordinates of points whose Cartesian co-ordinates are: (-√3,1)

Answer»

(x, y) = (- √ 3, 1)

∴ r = \(\sqrt{x^2+y^2} = \sqrt{3+1}=\sqrt4=2\)

tan θ = \(\frac{y}{x} = \frac {1}{-\sqrt3}=-tan \frac{\pi}{6}\)

Since the given point lies in the 2nd quadrant,

tan θ = tan (π-π/6) …[∵ tan (π – x) = – tan x]

∴ tan θ = tan (5π/6)

∴ θ = (5π/6)= 150°

∴ the required polar co-ordinates are (2, 150°)