# Resolution of fundamental trigonometric inequalities

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)

For example, when we solve the inequality sen x> sen or sen x> 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:

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