Question

How do you find the polar coordinates given the rectangular coordinates `(-2,-5)`?

Answer 1

`(sqrt29,4.33)`

Explanation:

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

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

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

and `color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))`

here x = - 2 and y = - 5

`rArrr=sqrt((-2)^2+(-5)^2)=sqrt(4+25)=sqrt29`

Now (-2 ,-5) is in the third quadrant so we must ensure that `theta` is in the third quadrant.

`theta=tan^-1(5/2)=1.19" radians"larr" reference angle"`

`rArrtheta=(pi+1.19)=4.33`

`rArr(-2,-5)to(sqrt29,4.33)to(sqrt29,248.2^@)`