This　technical　note　addresses　the　cooperative　global　output　regulation　problem　for　second-order　nonlinear　multi-agent　systems　without　a　priori　knowledge　of　the　control　direction.　We　will　propose　both　the　graph-dependent　and　graph-independent　distributed　controllers　based　on　the　combination　of　the　internal　model,　the　Nussbaum-type　dynamic　gain,　and　the　adaptive　control　technique.　Comparing　with　some　existing　results,　our　novel　design　can　handle　the　multi-agent　system　with　not　only　the　arbitrary　and　non-identical　unknown　control　direction　but　also　the　uncertain　parameter　that　belongs　to　any　unknown　and　non-compact　set.