Trigonometry Examples

Find the Domain and Range f(x)=2csc(x/2)
Step 1
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 2
Solve for .
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Step 2.1
Multiply both sides of the equation by .
Step 2.2
Simplify both sides of the equation.
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Step 2.2.1
Simplify the left side.
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Step 2.2.1.1
Cancel the common factor of .
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Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Rewrite the expression.
Step 2.2.2
Simplify the right side.
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Step 2.2.2.1
Remove parentheses.
Step 3
The domain is all values of that make the expression defined.
Set-Builder Notation:
, for any integer
Step 4
The range is the set of all valid values. Use the graph to find the range.
Interval Notation:
Set-Builder Notation:
Step 5
Determine the domain and range.
Domain: , for any integer
Range:
Step 6