Question

Despite some initial concerns, the teacher is confident that her students mastered the lesson.

This is a sentence.
Here the teacher is confident is the independent clause and that her students mastered the lesson is a dependent clause(Noun Clause) .
My question is that the dependent clause here is modifying or giving more information about the adjective confident (Why the teacher is happy?)
and therefore (that her students have mastered the lesson ) should be a adverbial clause as it behaves like an adverb by modifying adjective confident .
CORRECT ME I AM WRONG

Answer 1

that her students mastered the lesson is a noun clause

Step-by-step explanation:

A noun clause is a dependent clause that acts as a noun.

First of all, confident does not mean 'happy'. Confident means having full assurance.

Compare the two sentences:

1. He was confident of success. 2. He was confident that he would succeed.

The word success is a noun, and the clause that he would succeed acts as a noun, too.

In your sentence,

The teacher is confident means the teacher is certain (almost knows for sure) that her students mastered the lesson.

You may ask: What is the teacher confident of?

The teacher is confident of her students' mastery. (...that her students mastered the lesson.)

The word mastery is a noun, and the clause that her students mastered the lesson acts as a noun, too.

So the given clause acts as a noun and, therefore, is not an adverbial clause but a noun clause.