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

##### 1 Answer

Feb 18, 2016

# (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"#