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

## Homework Statement

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

1. |sinX|<0.5

2. |cosX|>0.5

## 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.

LCKurtz
Science Advisor
Homework Helper
Gold Member

## Homework Statement

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

1. |sinX|<0.5

2. |cosX|>0.5

## 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

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

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.

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.

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

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

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.

Can I arrive to that algebraically?

LCKurtz
Science Advisor
Homework Helper
Gold Member
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.

Can I arrive to that algebraically?

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?

SammyS
Staff Emeritus
Science Advisor
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Gold Member
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.

Thank you for the answers, people.