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Trigonometry Examples
Step 1
Step 1.1
Simplify each term.
Step 1.1.1
Use the Binomial Theorem.
Step 1.1.2
Simplify each term.
Step 1.1.2.1
Rewrite as .
Step 1.1.2.1.1
Use to rewrite as .
Step 1.1.2.1.2
Apply the power rule and multiply exponents, .
Step 1.1.2.1.3
Combine and .
Step 1.1.2.1.4
Cancel the common factor of and .
Step 1.1.2.1.4.1
Factor out of .
Step 1.1.2.1.4.2
Cancel the common factors.
Step 1.1.2.1.4.2.1
Factor out of .
Step 1.1.2.1.4.2.2
Cancel the common factor.
Step 1.1.2.1.4.2.3
Rewrite the expression.
Step 1.1.2.1.4.2.4
Divide by .
Step 1.1.2.2
Rewrite as .
Step 1.1.2.3
Factor out .
Step 1.1.2.4
Pull terms out from under the radical.
Step 1.1.2.5
Multiply by .
Step 1.1.2.6
Rewrite as .
Step 1.1.2.6.1
Use to rewrite as .
Step 1.1.2.6.2
Apply the power rule and multiply exponents, .
Step 1.1.2.6.3
Combine and .
Step 1.1.2.6.4
Cancel the common factor of .
Step 1.1.2.6.4.1
Cancel the common factor.
Step 1.1.2.6.4.2
Rewrite the expression.
Step 1.1.2.6.5
Simplify.
Step 1.1.2.7
Raise to the power of .
Step 1.1.2.8
Multiply by .
Step 1.1.2.9
Raise to the power of .
Step 1.1.2.10
Multiply by .
Step 1.1.2.11
Raise to the power of .
Step 1.2
Simplify the expression.
Step 1.2.1
Add and .
Step 1.2.2
Move .
Step 2
Step 2.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2.2
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Raising to any positive power yields .
Step 3.2.1.2
Multiply by .
Step 3.2.1.3
Multiply by .
Step 3.2.1.4
Rewrite as .
Step 3.2.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.1.6
Multiply by .
Step 3.2.1.7
Rewrite as .
Step 3.2.1.8
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.1.9
Multiply by .
Step 3.2.2
Simplify by adding numbers.
Step 3.2.2.1
Add and .
Step 3.2.2.2
Add and .
Step 3.2.2.3
Add and .
Step 3.2.2.4
Add and .
Step 3.2.3
The final answer is .
Step 4
The radical expression end point is .
Step 5
Step 5.1
Substitute the value into . In this case, the point is .
Step 5.1.1
Replace the variable with in the expression.
Step 5.1.2
Simplify the result.
Step 5.1.2.1
Simplify each term.
Step 5.1.2.1.1
One to any power is one.
Step 5.1.2.1.2
Multiply by .
Step 5.1.2.1.3
Multiply by .
Step 5.1.2.1.4
Any root of is .
Step 5.1.2.1.5
Multiply by .
Step 5.1.2.1.6
Any root of is .
Step 5.1.2.1.7
Multiply by .
Step 5.1.2.2
Simplify by adding and subtracting.
Step 5.1.2.2.1
Add and .
Step 5.1.2.2.2
Subtract from .
Step 5.1.2.2.3
Subtract from .
Step 5.1.2.2.4
Add and .
Step 5.1.2.3
The final answer is .
Step 5.2
Substitute the value into . In this case, the point is .
Step 5.2.1
Replace the variable with in the expression.
Step 5.2.2
Simplify the result.
Step 5.2.2.1
Simplify each term.
Step 5.2.2.1.1
Raise to the power of .
Step 5.2.2.1.2
Multiply by .
Step 5.2.2.1.3
Multiply by .
Step 5.2.2.2
Simplify by adding terms.
Step 5.2.2.2.1
Add and .
Step 5.2.2.2.2
Add and .
Step 5.2.2.2.3
Subtract from .
Step 5.2.2.3
The final answer is .
Step 5.3
The square root can be graphed using the points around the vertex
Step 6