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