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Trigonometry Examples
Step 1
Combine and .
Step 2
Combine and .
Step 3
Step 3.1
Subtract from both sides of the inequality.
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
Multiply by .
Step 3.4.4
Multiply by .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
Simplify each term.
Step 3.6.1
Simplify the numerator.
Step 3.6.1.1
Factor out of .
Step 3.6.1.1.1
Factor out of .
Step 3.6.1.1.2
Factor out of .
Step 3.6.1.1.3
Factor out of .
Step 3.6.1.2
Multiply by .
Step 3.6.1.3
Multiply by .
Step 3.6.1.4
Subtract from .
Step 3.6.2
Move to the left of .
Step 3.6.3
Move the negative in front of the fraction.
Step 4
Add to both sides of the inequality.
Step 5
Step 5.1
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 5.2
Simplify the left side.
Step 5.2.1
Dividing two negative values results in a positive value.
Step 5.2.2
Divide by .
Step 5.3
Simplify the right side.
Step 5.3.1
Move the negative one from the denominator of .
Step 5.3.2
Rewrite as .
Step 6
Multiply both sides by .
Step 7
Step 7.1
Simplify the left side.
Step 7.1.1
Cancel the common factor of .
Step 7.1.1.1
Cancel the common factor.
Step 7.1.1.2
Rewrite the expression.
Step 7.2
Simplify the right side.
Step 7.2.1
Simplify .
Step 7.2.1.1
Cancel the common factor of .
Step 7.2.1.1.1
Move the leading negative in into the numerator.
Step 7.2.1.1.2
Factor out of .
Step 7.2.1.1.3
Cancel the common factor.
Step 7.2.1.1.4
Rewrite the expression.
Step 7.2.1.2
Multiply by .
Step 8
The result can be shown in multiple forms.
Inequality Form:
Interval Notation: