Question

I'm stuck at something. How did this person get (5, pi/3) = (5, -5pi/3)=(-5, 4pi/3) = (-5, -2pi/3)
link: http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx

Answer 1

I know we're not meant to just give answers but it seems that you just need an explanation as to why this happens.

With polar co-ordinates the first number in the brackets tells us the radius (how far away from the centre the point is) and the second tells us the anti-clockwise rotation around the x-axis. We can get an infinite number of co-ordinates to describe any one point by ADDING MULTIPLES OF 2pi TO IT. This is because 2pi describes a full turn.

The reason (5, pi/3) and (5, -5pi/3) describe the same point is because if we add -2pi to (5, pi/3) we get (5, -5pi/3).

The reason (-5, -2pi/3) is the same as (5, pi/3) is that they both have the same radius and they are both the same rotation away from the x-axis (pi/3). For (-5,-2pi/3) you can see that we go pi/3 anticlockwise from the negative x-axis.

This is a difficult concept to understand, if there's any way I can clarify this point then please let me know.

Answer 2

yeah. I'm new when it comes to Calculus III material. Some parts of this may have something to do with Trig. with the circle and the values like 90 degrees in radians is pi/2 180 degrees in radians is pi and so on.

Answer 3

where did that person get the 5 pi from? Unless I'm supposed to subtract 2pi or something....