The main emphasis of Rosh Hashana is to establish that Hashem is King of the universe. There is no mention in all of the prayers of our sinning and the need for repentance.
The idea here is that Hashem's place in the world must first be established. Only when we recognize His awesome power, and that every living being in this world depends on Him for survival, can we begin to understand the need to ask for forgiveness for our sins.
Rosh Hashana is meant to move us and perhaps frighten us. When we read the ונתנה תקף prayer that describes even the solemnity taking place in Heaven among the angels, we are meant to be moved. The angels themselves express fear of the awesomeness of the Day of Judgement.
We are compared to a herd of sheep and Hashem is the shepherd. He randomly decides which sheep shall live and which will die.
Hashem is established as King on Rosh Hashana and we are established as His loyal subjects. May we all be inscribed for a healthy and happy New Year. Shana Tova to all.