Rabbi Roodyn

‘ו) בַּחֲצֹצְרוֹת וְקוֹל שׁוֹפָר הָרִיעוּ לִפְנֵי הַמֶּלֶךְ ה

With trumpets and the sound of a shofar, raise your voices before the King, Hashem.

Rav Hirsch says that the chatzotzros referred to are the instruments referred to in Bamidbar 10:10 that are employed to summon men to the aid of others and to ‘summon’ Hashem to the aid of mankind.

The shofar, on the other hand is used by Hashem to call man to Himself and man makes use of it in the name of G-d to summon himself and his fellows to follow Hashem and to serve Him in humble obedience.