Question

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

Answer 1

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

Explanation:

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

`"that is "(x,y)to(r,theta)" where"`

`•color(white)(x)r=sqrt(x^2+y^2)`

`•color(white)(x)theta=tan^-1(y/x);-pi< theta<= pi`

`"here "x=-3" and y=3`

`rArrr=sqrt((-3)^2+3^2)=sqrt18=3sqrt2`

`(-3,3)" is in the second quadrant so "theta" must be in the "`
`"second quadrant"`

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

`rArrtheta=pi-pi/4=(3pi)/4larrcolor(red)"in second quadrant"`

`rArr(-3,3)to(3sqrt2,(3pi)/4)`