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: (-1, -1)
Answer» (x, y) = (-1, -1) ∴ r = \(\sqrt {x^2+y^2} = \sqrt{1+1}=\sqrt2\) tan θ = \(\frac{y}{x} = \frac {-1}{-1}=1\) ∴ tan θ = tan π/4 Since the given point lies in the 3rd quadrant, tan θ = tan (π + π/4) …[∵ tan (n + x) = tan x] ∴ tan θ = tan (5π/4) ∴ θ = (5π/4) = 225° ∴ the required polar co-ordinates are ( \(\sqrt2\), 225°).

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

Answer»

(x, y) = (-1, -1)

∴ r = \(\sqrt {x^2+y^2} = \sqrt{1+1}=\sqrt2\)

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

∴ tan θ = tan π/4

Since the given point lies in the 3rd quadrant,

tan θ = tan (π + π/4) …[∵ tan (n + x) = tan x]

∴ tan θ = tan (5π/4)

∴ θ = (5π/4) = 225°

∴ the required polar co-ordinates are ( \(\sqrt2\), 225°).