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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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What is cos of a negative angle?
The cosine function is an even function which means that cos(-x) = cos(x). So, if cos of an angle is positive, then the cos of the negative of that angle is positive and if cos of an angle is negative, then the cos of the negative of that angle is negaitive.
When dividing a positive number by a negative number what is the results?
A negative number results when dividing a positive number by a negative number.
Does cos x equal cos negative x?
Yes. Cosine is adjacent side over hypothenuse. Adjacent side is the same sign when x is positive or negative.
Does negative times a negative times a negative equal a positive?
No - it results in a negative number.
Is a positive plus a negative make a positive or a negative?
Positive + Negative = Negative Negative + Negative = Positive Positive + Positive = Positive Negative + Positive = Negative
