non-numerical definition
non-numerical means that we can characterize the angle with no number, but considering it as an angle of a triangle or so, which is still sufficient for a deter- mination of its sine and cosine (see, e.g., Fig. 1). Still the sine and cosine can also be considered as numerical functions of a certain parameterization of the angle, i.e., functions such that if we know their argument we can obtain their value through a certain calculation without any geometric manipulations.