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# Trigonometry Examples

Remove the absolute value term. This creates a on the right side of the inequality because .

Set up the positive portion of the solution.

Move all terms not containing to the right side of the inequality.

Subtract from both sides of the inequality.

Subtract from .

Divide each term by and simplify.

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Set up the negative portion of the solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.

Move all terms not containing to the right side of the inequality.

Subtract from both sides of the inequality.

Subtract from .

Divide each term by and simplify.

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Set up the union.

or

Use each root to create test intervals.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is less than the right side , which means that the given statement is false.

False

False

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Compare the intervals to determine which ones satisfy the original inequality.

True

False

True

True

False

True

The solution consists of all of the true intervals.

or

Convert the inequality to interval notation.