Question

How do you find the polar coordinates given `(1,-1)`?

Answer 1

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

Explanation:

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

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 4th quadrant so we must ensure that `theta` is in the 4th quadrant.

`theta=tan^-1(-1)=-pi/4" in 4th quadrant"`

`rArr(1,-1)to(sqrt2,-pi/4)`