Trig is basically to do with triangles and circles. It works from the properties of angles relative to the sides of triangles and how these can be seen in circles (unit circles - with a radius of 1). It's used to tell you the size of angles and sides using other information you already know about the triangle.
The trig identities, I reckon, are probably best defined as ratios.
All fractions are ratios, as well as being processes.
For a right angled triangle (where we tend to begin with these)
Cos = adjacent/hypotenuse
Tan = opposite/adjacent
For each angle, there will be a different value for each one of these. So sin 42 will be the same whatever triangle you have. It regulates what the sizes of the opposite and hypotenuse will be only in terms of the ratio between them.
Sin and Cos (not sure about Tan) will always give a value between 1 and -1 inclusive.