In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side of that angle to the hypotenuse.
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That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).
Tan of pi/2 + k*pi radians, for integer k, is not defined since tan = sin/cos and the cosine of these angles is 0. Since divsiion by 0 is not defined, the tan ratio is not defined.
Inverse of Cosine is 'ArcCos' or Cos^(-1) The reciprocal of Cosine is !/ Cosine = Secant.
The range of cosine is [-1, 1] which is, therefore, the domain of cos-1. As a result, cos-1(2) is not defined.