Which type of headache is characterized by a unilateral throbbing pain?

The type of headache characterized by unilateral throbbing pain is the migraine headache. Migraines often present as a moderate to severe pain that typically affects one side of the head, although they can sometimes be bilateral. This type of pain is often described as pulsating or throbbing, and it can be accompanied by other symptoms such as nausea, vomiting, and sensitivity to light and sound.

In contrast, tension headaches tend to present as a dull, aching pain that is usually bilateral and is often described as a feeling of pressure or tightness around the head, rather than a throbbing sensation. Sinus headaches are generally associated with sinus infections and are characterized by pain in the forehead, cheeks, and around the eyes, often worsened by bending forward or sudden movement, and are typically not described as throbbing. Cluster headaches, while they can cause severe unilateral pain, are usually sharp or burning rather than throbbing and occur in cyclical patterns known as cluster periods.

Therefore, the distinct features of a migraine headache, especially the unilateral throbbing nature of the pain, make it the correct answer to this question.