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?

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;

where;

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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