00:02
Okay, in this problem we have two polar coordinates.
00:06
The first one is two and a half meters at an angle of 30 degrees measured from the positive x -axis.
00:16
And the second one has a distance of 3 .8 meters at an angle of 120 degrees.
00:25
And the first question is what are the cartesian coordinates of these two points.
00:31
So if we look at this first point right here and we think about it as a right triangle, we can see that the x value is going to be 2 .5 times the cosine because we're dealing with the adjacent of 30 degrees.
00:50
And the y is going to be 2 .5 times the sign of 30 degrees.
00:56
And when we plug these into our calculator, we get 2 .17 meters and 1 .24.
01:02
Meters for the cartesian coordinates of those two points so we can write that down right here 2 .17 meters and 1 .25 meters for the first point for the second point we do very very similar we've got 3 .8 times the cosine of 120 degrees and the advantage of using this as opposed to just trying to make it a small triangle is this will give us the minus sign that we need and we don't have to think about it and so when we do that math, that's minus 1 .9 meters.
01:37
And when we calculate the y value, which is this right here, that's going to be 3 .8 times the sign of 120 degrees.
01:47
And when we use our calculators, that's 3 .29 meters.
01:53
And so that gives us a cartesian coordinate of minus 1 .9 meters and 3 .29 meters...