# How do you find the X-values of inequalites involving trig functions?

1. Nov 9, 2011

### graphs

1. The problem statement, all variables and given/known data

What values of X between 0 and 2 pie radians satisfy each of the following:

1. |sinX|<0.5

2. |cosX|>0.5

2. Relevant equations

3. The attempt at a solution

Well the values of X lie between

1. -0.5 < sinX <0.5

2. cosX< -0.5 and cosX>0.5

How do you find the actual values of X? Do you use inverse trig functions? I forgot all that. Please, someone show me how to find the X's. Thanks.

2. Nov 9, 2011

### LCKurtz

No, the values of x don't lie on those intervals. Those are the intervals where sin(x) and cos(x) lie.

Draw the graphs. You can easily see where the values of x are that work on the graph. Assuming you know what x gives sine or cosine of .5 it should be easy to write down the x intervals.

3. Nov 9, 2011

### graphs

Right. I made a mistake sin(X) or cos(X)= F(X)=Y...No X's. .

Can I arrive to that algebraically?

4. Nov 9, 2011

### LCKurtz

You can use the inverse cosine and sine functions to get the principle values. You still need to get the others. Can you not get the "standard triangle" angles and their sines and cosines by drawing little triangles?

5. Nov 9, 2011

### SammyS

Staff Emeritus
Solve |sin(x)| = 0.5 for 0 ≤ x ≤ 2π . Place the solutions on the x-axis. They divide the x-axis up into intervals. Since the |sin(x)| is a continuous function, |sin(x)| will be entirely above 0.5 or entirely below 0.5 in each interval, so pick a test point from each interval.

6. Nov 10, 2011

### graphs

Thank you for the answers, people.