Question

What is the polar form of `(-6,12)`?

Answer 1

`(6sqrt5 , 2.04)`

Explanation:

using formulae that links Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`•theta = tan^-1 (y/x)`

hence `r^2 = (-6)^2 + 12^2 = 36 + 144 = 180`

`r^2 = 180 rArr r = sqrt180 = 6sqrt5`

since (-6 , 12 ) is a point in the 2nd quadrant , care must be taken to

ensure that `thetacolor(black)(" is in the 2nd quadrant ")`

`theta = tan^-1(12/-6) = tan^-1(-2) = -1.1color(black)(" radians ")`

`rArr theta = (pi-1.1) ≈ 2.04color(black)(" radians ")`