My textbook defines sine and cosine functions of only oriented angles. For example cosine of an oriented angle is the signed abscissa / the radius of the circle. I've got two questions:
- Every time we meet the cosine of an angle, are we implicitly meaning that this angle is an oriented one, even if not specified? (i.e. the clockwise or counterclockwise sense matter even if we don't care)?
- When we talk about law of cosines, (i.e. c = sqrt( a^2 + b^2- 2ab*cosC)), the cosC is meant to be a cosine of an oriented angle C, even though orientation doesn't really matter?
They may sound odd questions, but they are not in physics context, where sign of angles matter and textbook basic definition are not so clear about that.