00:04
Number 55, we have a true or false question.
00:07
We're supposed to figure out whether or not every point has two polar coordinates.
00:12
And by that, i believe the question means, can you write the polar coordinates of the point in just two ways? so if you think something is false, all you need to do to prove it's false is to show one example.
00:26
We call it a counter example that proves it's false.
00:30
And i suspect this is false, and let me show you why.
00:32
So i'm going to actually choose one point.
00:36
I'm going to keep it simple.
00:38
How about if it's the point with radius one and the angle is 45 degrees? so are there just two ways to describe that point? is there just one other way to describe that point or more or less? well, i know that i will get to the exact same point.
01:00
If instead of just going 45 degrees, if i go that 45 degrees plus another 300 degrees, 60 degrees around the circle and back to the same place.
01:09
So that means another way to describe the point would be 1 for the radius and 405 degrees, which is from the 45 original degrees plus one time around the circle another 360.
01:25
Well, why couldn't i go all the way around the circle another time and go another 360 degrees and end up at the same point? so i would describe that with the same radius one and add another 360 degrees and get a total of 765 degrees...