Find all polar coordinates of point P where P = (3, -pi/3)
(3, negative pi divided by 3 + 2nπ) or (-3, negative pi divided by 3 + (2n + 1)π)
(3, negative pi divided by 3 + 2nπ) or (-3, negative pi divided by 3 + 2nπ)
(3, negative pi divided by 3 + 2nπ) or (3, negative pi divided by 3 + (2n + 1)π)
(3, negative pi divided by 3 + (2n + 1)π) or (-3, negative pi divided by 3 + 2nπ)
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@Luigi0210 do you know this?? :(
@Psymon I forgot this but I'm sure you remember it
Now of course if we have that point, (3, -pi/3), you can return back to that point by adding any multiple of 2pi. Nowit's the 2nd representation of the point we have to worry about. What polar coordinates of (r, theta) tell you to do is face in the same direction of theta, then move forward r units. Which is exactly what the drawing above represents. Facing in the direction of -pi/3, we move forward 3units.
Now given our other answer choices, they all include -pi/3. This mean we are forced to face -pi/3. Now in order to representthis point in a 2nd way, we have to have a negative r. So basically, we have to walk backwards 3 units and then somehow get back to the original point:
So inorder to get from where we are to the point we need to be add, we must add odd multiplies of pi. If we add an even multiple of pi, well end up at (-3,-pi/3), which is the wrong side ofthe circle. So the way to write it in a way in which we always get an odd numberis (2n+1)pi. That way no matter what n is, we always end up with an odd multiple of pi, which gets us to the point we want.