Question

How do you convert `(-1,1)` into polar form?

Answer 1

`(sqrt2,(3pi)/4)`

Explanation:

To convert from `color(blue)"cartesian to polar form"`

That is `(x,y)to(r,theta)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))`

and `color(red)(bar(ul(|color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))`

here x = -1 and y = 1

`rArrr=sqrt((-1)^2+1^2)=sqrt2`

Now (-1 ,1) is in the 2nd quadrant so we must ensure that `theta` is in the 2nd quadrant.

`theta=tan^-1(-1)=-pi/4larr" related acute angle"`

`rArrtheta=(pi-pi/4)=(3pi)/4`

Thus `(-1,1)to(sqrt2,(3pi)/4)`