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.
A dry, hacking cough may develop toward the end of a cold or after exposure to an irritant, such as dust or smoke. There are many causes of a nonproductive cough, such as: 1  Viral illnesses. 2  After a common cold, a dry cough may last several weeks longer than other symptoms and often gets worse at night. Infections. 2  An infection of the lungs or upper airway passages can cause a cough. 3  A productive cough may be a symptom of pneumonia, bronchitis, sinusitis, or tuberculosis. 4  Chronic lung disease.