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Question
Find the polar co-ordinates of the point whose Cartesian co-ordinates are.
`(3/2, (3√3)/2)`.
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Solution
`(3/2, (3√3)/2)`. = (x, y)
we have
r = `sqrt(x^2 + y^2)`
= `sqrt((3/2)^2 + (3sqrt3/2)^2)`
= `sqrt(9/4 + 27/4)`
= `sqrt(36/4)`
= `sqrt9`
r = 3
we have
x = r cosθ & y = r sinθ
`3/2` = 3 cosθ
cosθ = `3/(2xx3)`
cosθ = `1/2`
cosθ = cos `pi/3`
∴ θ lies in 1st quadarant
θ = `pi/3`
Required polar coordinates of the given point are `(3, pi/3)`.
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