Question

How do you convert the rectangular point `(4,-4sqrt3)` into polar form?

Answer 1

`(8,-pi/3)`

Explanation:

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

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

`•color(white)(x)r=sqrt(x^2+y^2)`

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

`"here "x=4" and " y=-4sqrt3`

`r=sqrt(4^2+(-4sqrt3)^2)=sqrt(16+48)=8`

`(4,-4sqrt3)" is in the fourth quadrant so we must ensure"`
`"that "theta" is in the fourth quadrant"`

`theta=tan^-1((4sqrt3)/4)`

`color(white)(theta)=tan^-1(sqrt3)=pi/3larrcolor(red)" related acute angle"`

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

`rArr(4,-4sqrt3)to(8,-pi/3)`