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 sinus infection can cause a headache or pressure in the eyes, nose, cheek area, or on one side of the head. A person with a sinus infection may also have a cough, sore throat, fever, bad breath, and nasal congestion with thick nasal secretions.