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Trigonometry Examples
Step 1
Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
Step 1.2.1
Cancel the common factor of .
Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 2
Step 2.1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Step 2.2
Subtract from both sides of the inequality.
Step 2.3
In the piece where is non-negative, remove the absolute value.
Step 2.4
To find the interval for the second piece, find where the inside of the absolute value is negative.
Step 2.5
Subtract from both sides of the inequality.
Step 2.6
In the piece where is negative, remove the absolute value and multiply by .
Step 2.7
Write as a piecewise.
Step 2.8
Apply the distributive property.
Step 3
Step 3.1
Move all terms not containing to the right side of the inequality.
Step 3.1.1
Subtract from both sides of the inequality.
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
To write as a fraction with a common denominator, multiply by .
Step 3.1.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 3.1.4.1
Multiply by .
Step 3.1.4.2
Multiply by .
Step 3.1.4.3
Multiply by .
Step 3.1.4.4
Multiply by .
Step 3.1.5
Combine the numerators over the common denominator.
Step 3.1.6
Simplify the numerator.
Step 3.1.6.1
Multiply by .
Step 3.1.6.2
Subtract from .
Step 3.2
Find the intersection of and .
Step 4
Step 4.1
Solve for .
Step 4.1.1
Move all terms not containing to the right side of the inequality.
Step 4.1.1.1
Add to both sides of the inequality.
Step 4.1.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.1.1.3
To write as a fraction with a common denominator, multiply by .
Step 4.1.1.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.1.1.4.1
Multiply by .
Step 4.1.1.4.2
Multiply by .
Step 4.1.1.4.3
Multiply by .
Step 4.1.1.4.4
Multiply by .
Step 4.1.1.5
Combine the numerators over the common denominator.
Step 4.1.1.6
Simplify the numerator.
Step 4.1.1.6.1
Multiply by .
Step 4.1.1.6.2
Add and .
Step 4.1.2
Divide each term in by and simplify.
Step 4.1.2.1
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.
Step 4.1.2.2
Simplify the left side.
Step 4.1.2.2.1
Dividing two negative values results in a positive value.
Step 4.1.2.2.2
Divide by .
Step 4.1.2.3
Simplify the right side.
Step 4.1.2.3.1
Move the negative one from the denominator of .
Step 4.1.2.3.2
Rewrite as .
Step 4.2
Find the intersection of and .
Step 5
Find the union of the solutions.
Step 6
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 7