Almost all trigonometric inequalities, when properly handled and transformed, can be reduced to at least one of the fundamental inequalities. Let us know them below by way of examples.

**1st case** : sen x <sen a (sen x sen a)

For example, when we resolve the inequality we initially found which is a particular solution in the range . Adding at the ends of the ranges found, we have the general solution in IR, which is:

The solution set is therefore:

On the other hand, if inequality were then simply include the ends of and the solution set would be:

**2nd case:** sen x> sen a (sen x sen a)

Adding at the ends of the ranges found, we have the general solution in IR, which is:

The solution set is therefore:

**3rd case:** cos x <cos a (cos x cos a)

Adding at the ends of the range found, we have the general solution in IR, which is:

The solution set is therefore:

On the other hand, if inequality were cos x waistband or cos x then simply include the ends of and the solution set would be:

Next: Resolving Inequalities (Part 2)