You can try to trip an opponent as an unarmed melee attack. You can only trip an opponent who is one size category larger than you, the same size, or smaller.
Making a Trip Attack
Make an unarmed melee touch attack against your target. This provokes an attack of opportunity from your target as normal for unarmed attacks.
So if a PC has Improved Unarmed Strike, which
Improved Unarmed Strike [General]
You are considered to be armed even when unarmed —that is, you do not provoke attacks of opportunity from armed opponents when you attack them while unarmed. However, you still get an attack of opportunity against any opponent who makes an unarmed attack on you.
In addition, your unarmed strikes can deal lethal or nonlethal damage, at your option.
Without this feat, you are considered unarmed when attacking with an unarmed strike, and you can deal only nonlethal damage with such an attack.
Would they still be considered "unarmed" when making a trip without a trip weapon? I am confused as it says it would be a "unarmed melee touch attack".