Clip (extract) coarse resolution raster to same outline of polygon (shapefile) arcmap
In this video, you can learn how to clip a raster that its pixel edges are coarser than your shapefile or polygon in Extract by Mask that gives you exact outline of the shapefile.
You need to have another raster that is very fine (you can find very fine DEM in OpenTopography).
You also need to have your coarse raster, fine raster, as well as your shapefile projected to a UTM system.
Also, you need your fine resolution raster to be clipped (extracted) to your shapefile.
then you go through Extract by mask, after choosing the raster to be extracted and the shafepile to extract according to, you go to environment - then, raster analysis -
in cell size, choose the fine raster you have
in mask, choose your shapefile
DONE