00:01
We now determine the coordinates of a point which makes an angle of 2405 degree on a circle of radius 20 units.
00:10
So here i have drawn the circle of radius 20 units and i have also indicated the angle 245 degree and this is the point p.
00:20
So using this point p we construct a right triangle.
00:24
That is we construct the right triangle oap where angle p -a -o -a -p where angle p -a -o is the right triangle and notice that this 245 degree is basically the sum of 180 degree plus 65 degree.
00:39
So i have also shown that on this red triangle.
00:42
So in place of finding 245 degree, we can consider that this is becoming a reference angle.
00:50
So we can utilize this reference angle to determine the coordinates x and y.
00:55
So i'm now going to use soca toa in the right triangle oab.
01:00
So let's consider the right triangle oap.
01:06
And i'm going to first find sign of 65.
01:10
This is sign of 65.
01:12
This equals opposite by adjacent.
01:15
That is opposite to 65 degree is ap, which is negative y, divided by hypotenuse is op.
01:25
So we can replace op.
01:27
That is this becomes negative y over ops basically the radius of the circle which is 20 units now let's solve for y from this equation so we have a sign of 65 degree and this equals a negative y over 20 so we multiply both size by 20 so this means we get a negative y equals a 20 times of sign of 65 so therefore we divide both size by negative one which gives us the positive value of y and this becomes negative of 20 times of sign of 65 degree.
02:06
So we can plug this into the calculator and when we do that we get the value of y as negative 18 .126...