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Trigonometry Examples
Step 1
Step 1.1
Set the denominator in equal to to find where the expression is undefined.
Step 1.2
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 1.3
The domain is all values of that make the expression defined.
Set-Builder Notation:
, for any integer
Set-Builder Notation:
, for any integer
Step 2
Step 2.1
Substitute the value into . In this case, the point is .
Step 2.1.1
Replace the variable with in the expression.
Step 2.1.2
Simplify the result.
Step 2.1.2.1
Simplify the numerator.
Step 2.1.2.1.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.1.2.1.2
Evaluate .
Step 2.1.2.2
Simplify the expression.
Step 2.1.2.2.1
Multiply by .
Step 2.1.2.2.2
Divide by .
Step 2.1.2.3
The final answer is .
Step 2.2
Substitute the value into . In this case, the point is .
Step 2.2.1
Replace the variable with in the expression.
Step 2.2.2
Simplify the result.
Step 2.2.2.1
Move the negative one from the denominator of .
Step 2.2.2.2
Rewrite as .
Step 2.2.2.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.2.2.4
Multiply by .
Step 2.2.2.5
Evaluate .
Step 2.2.2.6
The final answer is .
Step 2.3
Substitute the value into . In this case, the point is .
Step 2.3.1
Replace the variable with in the expression.
Step 2.3.2
Simplify the result.
Step 2.3.2.1
Simplify the numerator.
Step 2.3.2.1.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.3.2.1.2
Evaluate .
Step 2.3.2.2
Simplify the expression.
Step 2.3.2.2.1
Multiply by .
Step 2.3.2.2.2
Divide by .
Step 2.3.2.3
The final answer is .
Step 2.4
The absolute value can be graphed using the points around the vertex
Step 3