Question

How do you convert `(7sqrt3, -7)` into polar coordinates?

Answer 1

`(7sqrt3,-7)to(14,-pi/6)`

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)|)))`

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

here `x=7sqrt3" and " y=-7`

`r=sqrt((7sqrt3)^2+(-7)^2)=sqrt(147+49)=sqrt196=14`

Now `(7sqrt3,-7)` is in the 4th quadrant and care must be taken to ensure `theta` is in the 4th quadrant.

`theta=tan^-1(-7/(7sqrt3))=tan^-1(-1/sqrt3)=-pi/6" 4th quadrant"`

`rArr(7sqrt3,-7)=(14,-pi/6)=(14,-30^@)`