Question

The rectangular coordinates of a point are given `(4, -4sqrt3)`, how do you find polar coordinates of the point?

Answer 1

Use the formulas `x^2+y^2 = r^2` and `tan theta =y/x`

`r^2=(4)^2+(-4sqrt3)^2=16+48=64`

`r=sqrt64=8`

`tan theta = y/x=(-4sqrt3)/4=(-cancel(4)sqrt3)/cancel 4=-sqrt3`

`theta=tan^-1 -sqrt3=-pi/3`

`:.(r,theta)=(8,-pi/3)`