what is −3R+9U in polar form?

Answer 1

Coordinate is (-3,9). So the magnitude of the vector is the square root of the sum of squares which turns out to be 3Sqrt10. The angle is in the second quadrant where the tangent is equal to the opposite over the adjacent which in this case turns out to be a 9 divided by -3. This gives an inverse tangent equal to -3. So the reference angle for -3 is 71.6°. In the second quadrant it’s actually 108.4°. So the final polar form as I see it would be 3sqrt10 at an angle of 108.4°. It can also be represented as a negative value of the vector in the fourth quadrant. So one can identify this polar form as -3sqrt10 at an angle of (360-71.6)