Question

How do you convert `(2, -3)` into polar form?

Answer 1

`(2,-3)to(sqrt13,-0.983)`

Explanation:

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

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

`color(orange)"Reminders"`

`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 = 2 and y = -3

`rArrr=sqrt(2^2+(-3)^2)=sqrt13`

now (2 ,-3) is a point in the 4th quadrant so we must ensure that `theta` is in the 4th quadrant.

`theta=tan^-1(-3/2)=-0.983" in 4th quadrant "`

`rArr(2,-3)to(sqrt13,-0.983)=(sqrt13,-56.31^@)`