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# Trigonometry Examples

Subtract from both sides of the inequality.

Subtract from .

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

Multiply .

Multiply by .

Multiply by .

Multiply by .

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 .

Multiply each term in by

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

Multiply .

Multiply by .

Multiply by .

Multiply 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 .

Multiply each term in by

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

Multiply .

Multiply by .

Multiply by .

Multiply by .

Set up the intersection.

and

Find the intersection between the sets.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation: