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Trigonometry Examples
Step 1
Step 1.1
Expand using the FOIL Method.
Step 1.1.1
Apply the distributive property.
Step 1.1.2
Apply the distributive property.
Step 1.1.3
Apply the distributive property.
Step 1.2
Simplify and combine like terms.
Step 1.2.1
Simplify each term.
Step 1.2.1.1
Multiply by by adding the exponents.
Step 1.2.1.1.1
Move .
Step 1.2.1.1.2
Multiply by .
Step 1.2.1.2
Multiply by .
Step 1.2.1.3
Rewrite as .
Step 1.2.1.4
Multiply by .
Step 1.2.2
Subtract from .
Step 2
Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Subtract from .
Step 3
Convert the inequality to an equation.
Step 4
Use the quadratic formula to find the solutions.
Step 5
Substitute the values , , and into the quadratic formula and solve for .
Step 6
Step 6.1
Simplify the numerator.
Step 6.1.1
Raise to the power of .
Step 6.1.2
Multiply .
Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 6.1.3
Add and .
Step 6.1.4
Rewrite as .
Step 6.1.4.1
Factor out of .
Step 6.1.4.2
Rewrite as .
Step 6.1.5
Pull terms out from under the radical.
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 7
Consolidate the solutions.
Step 8
Use each root to create test intervals.
Step 9
Step 9.1
Test a value on the interval to see if it makes the inequality true.
Step 9.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.1.2
Replace with in the original inequality.
Step 9.1.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 9.2
Test a value on the interval to see if it makes the inequality true.
Step 9.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.2.2
Replace with in the original inequality.
Step 9.2.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 9.3
Test a value on the interval to see if it makes the inequality true.
Step 9.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.3.2
Replace with in the original inequality.
Step 9.3.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 9.4
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
Step 10
The solution consists of all of the true intervals.
Step 11
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 12