How do you express the Cartesian coordinates (0, - 3) as polar coordinates?

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Answer 1 · 2016-03-03T12:32:06

#(3,-(3pi)/2)#

Cartesian coordinates #(x,y)# can be written as polar coordinates as #(r,theta)#, where#r=sqrt(x^2+y^2)# and #theta=tan^-1(y/x)#.

Hence, #(0,-3)# can be written as

#(sqrt(0^2+(-3)^2), tan^-1(-3/0)# or #(3,tan^-1(-oo))#

#(3,-(3pi)/2)#

Answer 2 · 2016-03-03T13:23:47

#(3, 3pi/2)# or #(3, -pi/2)# or #(-3, pi/2)#

If r is reckoned positive, #theta# is either #3pi/2 or -pi/2#.
If the convention allows r to be negative, it could be in the third form..