Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) `(2,pi//3)` (ii) `(0.pi//2)` (iii) `(-sqrt(2),pi//4)`

Convert the following points from polar coordinates to the correspondi

1.	Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) `(2,pi//3)` (ii) `(0.pi//2)` (iii) `(-sqrt(2),pi//4)`
Answer» (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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Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) `(2,pi//3)` (ii) `(0.pi//2)` (iii) `(-sqrt(2),pi//4)`

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