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It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument.

As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to define the sine and the cosine functions.)

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Q: Why cos negative results positive?
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