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What is the distance between the following polar coordinates?: # (1,pi/2), (-1,pi/2) #

Answer 1

There must a mistake, polar coordinates of a point are given in the form #(rho, theta)#, where #rho# is the distance from the origin, and #theta# is the angle formed with the #x#-axis. So, #rho# can't be negative.

If you wanted to know the distance between

#(1,\pi/2)# and #(1,-\pi/2)#,

then you can work like this: since #rho=1#, both points are in the unit circle. And in particular, they are opposite points, since #90^@# and #-90^@# determine the "north pole" and "south pole" of the circle. So, the distance between them is two times the radius, which is #2#.

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Answer 2

Luke Alvarez

The distance between the polar coordinates (1, π/2) and (-1, π/2) is 2 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.