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Question
Find the polar co-ordinates of the point whose Cartesian co-ordinates are.
`(sqrt(2), sqrt(2))`
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Solution
Here `x = sqrt(2) and y = sqrt(2)`
∴ the point lies in the first quadrant.
Let the polar coordinates be (r, θ)
Then, r2 = x2 + y2 = (√2)2 + (√2)2 = 2 + 2 = 4
∴ r = 2 ...[ ∵ r > 0]
cos θ = `x/r = (√2)/2 = 1/(√2)`
and
sin θ = `y/r = (√2)/2 = 1/(√2)`
Since the point lies in the first quadrant and
0 ≤ θ < 2π, tanθ = 1 = `tan pi/(4)`
∴ θ = `pi/(4)`
∴ the polar coordinates of the given point are `(2, pi/4)`.
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