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Trigonometry Examples
Step 1
Step 1.1
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 1.2
Divide each term in by and simplify.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Cancel the common factor of .
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 1.2.3.1.2
Multiply .
Step 1.2.3.1.2.1
Multiply by .
Step 1.2.3.1.2.2
Multiply by .
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
Since the domain is not all real numbers, is not continuous over all real numbers.
Not continuous
Step 3