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 a natural reflex that protects your lungs. Coughing helps clear your airways of lung irritants, such as smoke and mucus (a slimy substance). This helps prevent infections. A cough also can be a symptom of a medical problem. Prolonged coughing can cause unpleasant side effects, such as chest pain, exhaustion, light-headedness, and loss of bladder control.