I need a little help and sorry for the dumb question.

I need the calculation of the cosine of angles, but in degrees, and GH works only with radians.
I try to convert from Radians to Degrees, but the result is not exact. In this fall the cos (80) should be 0.17°

As you correctly state above, Grasshopper expects radians instead of degrees for trigonometrical operations. Degrees are for humans, computers prefer radians.

The cosine of 1.3962 radians is 0.1736 rad, but the cosine of 80 rad is cos(80 \% 2π) = cos(4.6017) = -0.1103 rad.
Here the \%-symbol represent the modulo operator, which calculates the remainder of a dividend and divisor value, what is “left over”. Since 2π (i.e. 360°) is a full rotation around an imaginary circle, 80 rad represents 80 / 2π = 6.28, 6 full rotations plus an unfinished one. The cosine however is equal to the last rotation that is smaller than 2π. Its angle is 4.6017rad.

That isn’t strictly true (although probably good practise): you can flag input fields as taking degrees by right clicking on them and selecting the degree option (where available) resulting in (a) below.

Also, in formulae where you can’t, you can optionally use the rad() function inline, instead of the external Radians component, as at (b).