Your problem presentation is extremely confusing. I'm guessing that you're talking about
the right triangle formed when a vertical (from a pt on the unit circle) is drawn to the
When you're referencing the adjacent side(component of the x-axis)
and the hypotenuse (1 in the unit circle) of the central angle formed by the (rotating)
terminal side (with the x-axis) the trig function is COSINE (or its reciprocal, secant).
A COSINE function for a right triangle is adjacent side over hypotenuse. IF you
require an INVERSE cosine FUNCTION, you restrict the range to [0, π]
A cosine function has the domain of all real numbers (in which case the cosine
argument is called "radian" units. [degree units are more useful in practical
applications of trig]. The range of the cosine function is [-1, +1]
A sine function is the opposite side (a vertical) over the hypotenuse.
As long as you're referencing a central angle in a unit circle, the adjacent side
will be some component length of the x-axis; the opposite side will be a vertical
drawn from the unit circle to the x-axis.
When you refer to an adjacent side to a hypotenuse there is ambiguity, because
it's unclear which angle in the right triangle is being referenced. An adjacent
side in a right triangle must reference a short side (and the hypotenuse) that
form the angle; the side opposite, references the (shorter than hyp) side that's
not used to form the angle.