00:01
Okay, so first i'm going to draw an xy axis.
00:06
Here's the y axis.
00:07
Here's the x -axis.
00:09
And this is the radar station right here at the origin.
00:14
And due east is this axis right here.
00:17
So it's standard to using any trig function is to consider the positive x -axis, the zero degrees.
00:28
So if you want polar coordinates for this airplane at 10.
00:34
In 1015, you're 80 miles away and 25 degrees north of dewey.
00:39
So you're here where the length of this line is 80.
00:45
And therefore, in polar coordinates, x is equal to r cosine theta, r being, in this case, 80, the radius from the origin, the center.
01:00
And theta being the angle from the positive x axis.
01:04
So again, this is 25.
01:07
And y is r sine theta where r and theta are the same thing as with x so you can say that this point in polar coordinates is 80 cosine 25 degrees 80 sign 25 degrees and that's at 10 25 degrees and that's at 10 25 or no 1015 i'm wrong it's at 1015 and then at um you 1025, you're 110 miles away.
01:59
So this would be 110.
02:01
And this is 5 degrees south.
02:05
And so you can write that in polar coordinates as 110 cosine negative 5 degrees and 110 sign negative 5 degrees.
02:22
And so in polar coordinates, it's exactly what i've written here and here.
02:27
So those are your polar coordinates.
02:29
To get rectangular coordinates, you just enter those into a calculator.
02:32
So i'm going to go to desmos .com and use the scientific calculator.
02:38
And i'm going to say 80 cosine 25.
02:42
I wonder what that is.
02:44
80 cosine 25.
02:46
Let me make sure i'm in degrees.
02:47
I am.
02:48
So that's 72 .50.
02:51
How many decimal points do we need? we need two decimal places...