the rectangular coordinates of a point are given Find the po

the rectangular coordinates of a point are given. Find the polar coordinates (r,theta) of this pain with theta expressed in radians. let r>0 and 0<=theta,2pi (6,-6sqrt3)

Solution

(x,y)=(6,-6sqrt3)

x=rcos y=rsin

r=[x²+y²]

r=[(6)²+(-6sqrt3)²]

r=[(6)²+(6²*3)]

r=[144]

r =12

x>0,y<0

=2- tan^-1(y/x)

=2- tan^-1(63 /6)

=2- tan^-1(3)

=2- (/3)

=5/3

(r,)=(12,5/3)