In the image resize box, change the dpi to 360 (make sure the resample box is unchecked), ignore the dimension boxes. That will set your DPI to 360 with no resampling of the image (the 360 is just a number in metadata). Then in the square marquee tool, set the image size you want in inches in the appropriate boxes. When you click in the image, it will automatically create a crop box you can drag to where you want. When you click on crop in the image menu, that will give you an image the size you want at 360 dpi. That's the method I use, I am sure there are others which may be even simpler.