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