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 cough is your bodyâs natural reflex to help clear your airways of irritants and prevent infection. Common irritants include smoke, mucus, or allergens such as pollen, mold, or dust. Some medical conditions or medicines irritate the nerve endings in your airways and cause coughing. A cough may be acute, subacute, or chronic depending on how long it lasts.