In a coordinate system where the x-axis is east:

1. For what range of angles is the x-component positive?
2. For what range of angles is the x-component negative?

if i remeber correctly when dealing with real world cordinate systems as you rotate around clockwise you move in a positive direction. but all the examples i have done said north was 0 degrees, so i may be wrong

Answered by conungi | 2024-06-10

The positive x-values, the range of value of θ is between 0⁰ and 90⁰ , and for negative x-values, the range of value of θ is between 91⁰ and 180⁰ .
The x-components of vectors is given as;
x = x i ​ × cos ( θ )
where;

θ is the position of the vector

For positive x-values, the range of value of θ is between 0⁰ and 90⁰ .
cos (0) = 1
cos (90) = 0
For negative x-values, the range of value of θ is between 91⁰ and 180⁰ .
cos (91) = -0.017
cos (180) = -1
Thus, the positive x-values, the range of value of θ is between 0⁰ and 90⁰ , and for negative x-values, the range of value of θ is between 91⁰ and 180⁰ .
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Answered by onyebuchinnaji | 2024-06-15

The x-component of a vector is positive for angles between 0° and 90° and negative for angles between 90° and 180°. The sign of the x-component is determined by the cosine of the angle, which is positive in the first quadrant and negative in the second quadrant. Thus, the relevant ranges are 0° ≤ θ < 90° for positive and 90° < θ ≤ 180° for negative x-components.
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Answered by onyebuchinnaji | 2024-10-11