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.
Sinus headache. Introduction. Sinus headaches cause a dull, deep, throbbing pain in the front of your head and face. They are caused by an inflammation in your sinuses, air-filled cavities around your nose, eyes, and cheeks. Bending down or leaning over usually makes the pain worse, as does cold and damp weather. Sinus headaches often begin first thing in the morning, and may be better by afternoon. Sinus headaches can be difficult to diagnose, however, because symptoms are similar to tension headaches and migraines.