This is not a great question to be asking.

 

Think of the process on the whizz wheel. To get from CAS via EAS to TAS we use pressure altitude and temperature. To go back from TAS via EAS to CAS we would again use pressure altitude and temperature. You are correct when you say that temperature is a factor. However, it is the entry with pressure altitude and temperature which corrects for density errors (the fact that the ASI is calibrated to an atmospheric density value of 1225gm/cuM.); we do not use density altitude because we are correcting for the difference between 1225gm/cuM and actual density.

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