Trigonometry Examples

$\cot^{2} (x)$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the argument in $\cot (x)$ equal to $π n$ to find where the expression is undefined.

$x = π n$ , for any integer $n$

Step 1.2

The domain is all values of $x$ that make the expression defined.

Set-Builder Notation:

${x | x \neq π n}$ , for any integer $n$

Set-Builder Notation:

${x | x \neq π n}$ , for any integer $n$

Step 2

Since the domain is not all real numbers, $\cot^{2} (x)$ is not continuous over all real numbers.

Not continuous

Step 3