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Trigonometry Examples
Step 1
Step 1.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2
Add to both sides of the inequality.
Step 1.3
Set the denominator in equal to to find where the expression is undefined.
Step 1.4
Add to both sides of the equation.
Step 1.5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Subtract from .
Step 2.3
The expression contains a division by . The expression is undefined.
Undefined
Step 3
The radical expression end point is .
Step 4
Step 4.1
Substitute the value into . In this case, the point is .
Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
Step 4.1.2.1
Simplify the expression.
Step 4.1.2.1.1
Multiply by .
Step 4.1.2.1.2
Subtract from .
Step 4.1.2.2
Simplify the numerator.
Step 4.1.2.2.1
Subtract from .
Step 4.1.2.2.2
Any root of is .
Step 4.1.2.3
Simplify the expression.
Step 4.1.2.3.1
Multiply by .
Step 4.1.2.3.2
Divide by .
Step 4.1.2.4
The final answer is .
Step 4.2
Substitute the value into . In this case, the point is .
Step 4.2.1
Replace the variable with in the expression.
Step 4.2.2
Simplify the result.
Step 4.2.2.1
Simplify the expression.
Step 4.2.2.1.1
Multiply by .
Step 4.2.2.1.2
Subtract from .
Step 4.2.2.1.3
Subtract from .
Step 4.2.2.2
Cancel the common factor of and .
Step 4.2.2.2.1
Factor out of .
Step 4.2.2.2.2
Cancel the common factors.
Step 4.2.2.2.2.1
Factor out of .
Step 4.2.2.2.2.2
Cancel the common factor.
Step 4.2.2.2.2.3
Rewrite the expression.
Step 4.2.2.2.2.4
Divide by .
Step 4.2.2.3
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5