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Trigonometry Examples
Step 1
Step 1.1
Set the argument in greater than to find where the expression is defined.
Step 1.2
Solve for .
Step 1.2.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.2
Set equal to and solve for .
Step 1.2.2.1
Set equal to .
Step 1.2.2.2
Solve for .
Step 1.2.2.2.1
Remove the absolute value term. This creates a on the right side of the equation because .
Step 1.2.2.2.2
Plus or minus is .
Step 1.2.3
The final solution is all the values that make true.
Step 1.2.4
Find the domain of .
Step 1.2.4.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2.4.2
The domain is all values of that make the expression defined.
Step 1.2.5
The solution consists of all of the true intervals.
Step 1.3
Set the radicand in greater than or equal to to find where the expression is defined.
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
Remove parentheses.
Step 2.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.4
Multiply by .
Step 2.5
Rewrite as .
Step 2.6
Pull terms out from under the radical, assuming positive real numbers.
Step 2.7
Multiply by .
Step 2.8
The logarithm of zero 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
Remove parentheses.
Step 4.1.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.1.2.3
Multiply by .
Step 4.1.2.4
Any root of is .
Step 4.1.2.5
Multiply by .
Step 4.1.2.6
Logarithm base of is .
Step 4.1.2.7
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
Remove parentheses.
Step 4.2.2.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.2.2.3
Multiply by .
Step 4.2.2.4
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5