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Question
Find the Cartesian co-ordinates of the point whose polar co-ordinates are:
`(1/2, (7pi)/3)`
Solution
Here, `r = 1/2 and θ = (7pi)/3`
Let the cartesian coordinates be (x, y)
Then,
`x = r cos θ = 1/2cos (7pi)/(3) = 1/2cos(2pi + pi/3)`
= `1/2cos pi/(3) = 1/2 xx 1/2 = 1/4`
`y = r sin θ = 1/2sin (7pi)/(3) = 1/2sin(2pi + pi/3)`
`= 1/2sin pi/(3) = 1/2 xx sqrt(3)/(2) = sqrt(3)/(4)`
∴ The cartesian coordinates of the given point are `(1/4, sqrt(3)/4)`.
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