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 headaches cause the front of your head and face to hurt. These are caused due to inflammation in the sinus passages behind the cheeks, nose, and eyes. The pain is usually worse in the mornings and when you bend forward. You may have postnasal drip, sore throat, and nasal discharge as well.