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.
Many times when there is a change in weather, especially if it is onset of dry weather, then it leads to dryness in the upper portion of the throat. Sometimes, that also causes cough. Asthma: Asthma is another common cause of coughing. In such a case, inflammation of the pharynx or larynx causes cough and eventually, start a headache.