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Convert the following points from polar ...

Convert the following points from polar coordinates to the corresponding Cartesian coordinates.
`(2,pi//3)`

Text Solution

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(i) `(2,pi//3)-=(r,theta)`
We have ` x=rcostheta=2"cos"(pi)/(3)=2xx(1)/(2)=1`
and `y=rsintheta=2"sin"(pi)/(3)=2xxsqrt(3)/(2)=sqrt(3)`
Therefore, the point is `(1,sqrt(3)` in the Cartesian coordinates.
(iii) `x=-sqrt(2) "cos"(pi)/(4)=-sqrt(2)((1)/(sqrt2))=-1`
`y=-sqrt(2)"sin"(pi)/(4) =-sqrt(2)((1)/(sqrt2))=-1`
So, the equivalent Cartesian coordinates for the given polar coordinates are `(-1,-1)`.
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