It would help if I knew a little more information about what you're looking for, in order to better answer your question, but here are the basics.
For a right triangle, given one of the angles that is not the 90° angle:
One way to remember this is: Sine, Cosine, Tangent; then think of Old Harry Always Has Old Apples. Sine = O/H, Cosine = A/H, and Tangent = O/A,
where O is the Opposite side, A is the Adjacent side, and H = Hypotenuse.
Another one that somebody taught me is: Oh Heck Another Hour Of Algebra. Pick whatever helps you to remember.
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The derivative of negative cosine is positive sine.
Cosine squared theta = 1 + Sine squared theta
its short for sine. theres sine, cosine, and tangent. sine is opposite over adjacent for the sides of a triangle (or angles)
Yes they are. Both have a a period of 2 pi
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.)