consider the vector F1: (27N,20°)The angles are measured from the positive x axis with the counter-clockwise angular direction taken as positive.
Consider the vector:F2=-F1
What is in degrees as measured from the positive x in the counter-clockwise angular direction the direction of vector F2?
*I have tried using the formula arctan (y/x)+ 180 but it keeps telling me I am incorrect. I would love it if anyone could give me some guidance on this.
F1 = 27N[20o] = 27*cos20 + i27*sin20 =
25.37 + 9.23i.
F2 = -27N[20o] = -27*cos20 - 27*sin20 =
-25.37 - -9.23i
Tan Ar = Y/X = -9.23/-25.37 = 0.36382
Ar = 20o = Reference Angle.
Since X and Y are both negative, we are in the 3rd Quad.
A = 20 + 180 = 200o = The direction of
F2.
To determine the direction of vector F2, you can use the concept of adding 180 degrees to the angle of vector F1. However, the formula you provided, arctan(y/x) + 180, is used for finding the angle of a vector in the clockwise direction from the positive x-axis.
In this case, vector F2 is the negative of vector F1, which means it has the same magnitude but the opposite direction. In terms of angles, this is equivalent to adding 180 degrees to the angle of F1 in the counterclockwise direction.
Here's the correct approach to find the direction of vector F2:
1. Start with the given angle of vector F1 as measured counterclockwise from the positive x-axis, which is 20 degrees in this case.
2. Add 180 degrees to the angle of F1.
Angle of F2 = Angle of F1 + 180 degrees
= 20 degrees + 180 degrees
= 200 degrees
Therefore, the direction of vector F2 as measured counterclockwise from the positive x-axis is 200 degrees.