Question

How do you convert `(-1,-3)` from cartesian to polar coordinates?

Answer 1

`(sqrt10,-1.893)`

Explanation:

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

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

`•color(white)(x)r=sqrt(x^2+y^2)`

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

`"here "x=-1" and "y=-3`

`rArrr=sqrt((-1)^2+(-3)^2)=sqrt10`

`theta=tan^-1(3)=1.249larrcolor(blue)"related acute angle"`

`(-1,-3)" is in the third quadrant so "theta" must be in the"`
`"the third quadrant"`

`rArrtheta=(-pi+1.249)=-1.893`

`rArr(-1,-3)to(sqrt10,-1.893)`