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