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: (5, 5)
Answer» (x, y) = (5, 5) ∴ r = \(\sqrt{x^2+y^2} = \sqrt{25+25}\) = \(\sqrt{50} = 5\sqrt{2}\) tan θ = y/x = 5/5 = 1 Since the given point lies in the 1st quadrant, θ = 45° …[∵ tan 45° = 1] ∴ the required polar co-ordinates are ( \(5\sqrt{2}\), 45°).

Find the polar co-ordinates of points whose Cartesian co-ordinates are: (5, 5)

Answer»

(x, y) = (5, 5)

∴ r = \(\sqrt{x^2+y^2} = \sqrt{25+25}\)

= \(\sqrt{50} = 5\sqrt{2}\)

tan θ = y/x = 5/5 = 1

Since the given point lies in the 1st quadrant,

θ = 45° …[∵ tan 45° = 1]

∴ the required polar co-ordinates are ( \(5\sqrt{2}\), 45°).