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.
Sinusitis occurs when your sinuses become inflamed, sometimes after you come down with a virus or bacterial infection. You might have sinusitis if you develop a fever, cough, nasal congestion, or postnasal drip at the same time. Sometimes sinusitis can make your head hurt, or make your sinuses feel sore.