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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
Set the denominator in equal to to find where the expression is undefined.
Step 1.3
Solve for .
Step 1.3.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.3.2
Simplify .
Step 1.3.2.1
Rewrite as .
Step 1.3.2.2
Pull terms out from under the radical, assuming real numbers.
Step 1.4
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
Raising to any positive power yields .
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
Any root of is .
Step 4.1.2.2
One to any power is one.
Step 4.1.2.3
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
Raise to the power of .
Step 4.2.2.2
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5