As a new user, often I have used "active" (that is, not grayed out and non-functional) Environments when using ArcToolbox Tools and the operation is non-responsive. I wish I documented for my own record what I have seen along the way, but have not, still being somewhat confused as to whether it is because I am doing something wrong. Following are two recent examples.
 
1) Using a raster, I have seen where 

    Spatial Analyst > Extract by Polygon > Environments > Raster Analysis 
    and changing the cell size will not change the cell size; 

and

2) using a raster

    Data Management > Resample > Environments > Raster Analysis > 
    Mask will change the cell size but not mask.

 Since the combination of operations that are not allowed by ArcGIS do not result in grayed out inactive buttons or a warning message, is there some list that tells what Environment operations can and can't be done with the various ArcToolbox Tools?