It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
Coughing is an everyday act for many of us. It may be a sign of bronchitis, a reaction to smoke, or simply a natural reaction to clear that tickle in your throat. While a nuisance, coughing typically does not cause actual pain or distress. But for those who suffer from primary cough headache, coughing is a painful and burdensome act.