Question

How do you convert `(-2, 2sqrt3)` into polar coordinates?

Answer 1

`(4 , 2.09 )`

Explanation:

To convert Cartesian to Polar coordinates , use the formulae which links the 2 systems.

`• r^2 = x^2 + y^2`

`• theta = tan^-1 (y/x)`

here `x = - 2 and y = 2sqrt3`

`r^2 = (-2)^2 +(2sqrt3)^2 = 4+ 12 = 16 rArr r = sqrt16 = 4`

The point `(-2 , 2sqrt3) " is in 2nd quadrant "`
care must be taken to ensure that `theta " is in 2nd quadrant"`

`theta = tan^-1((2sqrt3) /-2) = tan^-1(-sqrt3) = - 1.05 " radians"`

hence `theta = (pi-1.05) = 2.09 " radians"`