If a vector A has components Ax > 0, and Ay < 0, the range of values the vector makes with the positive x - axis is 270° ≤ Ф ≤ 360°
If a vector A has components Ax > 0, and Ay < 0, to find the range the angle that this vector makes with the positive x-axis must be in, we proceed as follows.
We know that for a given vector with vertical complonents Ay and horizontalcomponent Ax, the angle the vector makes with the positive x - axis, Ф is given by
tanФ = Ay/Ax
Now, If the vector A has components Ax > 0, and Ay < 0, it means that
tanФ = Ay/Ax = negative/positive = -ve
- This implies that tanФ.
- Also, Ax > 0, and Ay < 0, implies that tanФ is in the 4th quadrant.
So, the range of values of Ф in the fourth quadrant is 270° ≤ Ф ≤ 360°
So, the range of values the vector makes with the positive x - axis is 270° ≤ Ф ≤ 360°