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In a coordinate system in which the x-axis is east, for what range of angles is the x- component positive? For what range is it negative?

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conungi

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

onyebuchinnaji

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;

\(x = x_i \times cos(\theta)\)

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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