The respiratory system functions to filter, warm, and humidify the air we breathe, and to supply cells with oxygen while removing carbon dioxide. In animals that breathe with lungs, air moves into the lungs through the trachea and then back out again. When each breath is completed, the lung still contains a volume of air, called the residual volume. Each inhalation adds additional air. Each exhalation removes approximately the same volume as was inhaled.
Normal breathing involves rhythmic inhaling and exhaling.
Therefore, we can quantify breathing using trigonometric equations. Changes in breathing, such as those due to increased activity, can then be measured. An apparatus called a spirometer is used to measure the volume of air inhaled and exhaled while breathing. A spirogram is the record of the changing volumes over time. The output of a spirogram can be quantified using trigonometric equations.