What is the distance between the following polar coordinates?: # (1,-pi), (1,pi) #

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Answer 1 · 2018-01-16T12:02:47

They are same point, so the distance between them is #0#.

Polar coordinates of point A is #r_1=1.0 , theta_1=-180^0#

Polar coordinates of point B is #r_2=1.0 , theta_2=180^0#

Cartesian coordinates of point A is #x_1=r_1 cos theta_1 #

or # x_1= 1.0 cos (-180) = -1, y_1=r_1 sin theta # or

#y_1=1sin 180=0 :. # Cartesian coordinates of

point A is #(x_1,y_1) or (-1,0)#

Cartesian coordinates of point B is #x_2=r_2 cos theta_2 #

or # x_2= 1.0 cos 180 = -1.0, y_2=r_2 sin theta_2 # or

#y_2=1.0 sin 180=0 #. Cartesian coordinates of

point B is #(x_2,y_2) or (-1.0,0)# . They are same point,

so the distance between them is #0#. [Ans]