Trigonometry Examples

$\tan (x)$

Step 1

Find the domain to determine if the expression is continuous.

Tap for more steps...

Step 1.1

Set the argument in $\tan (x)$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

$x = \frac{π}{2} + π n$ , for any integer $n$

Step 1.2

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

Set-Builder Notation:

${x | x \neq \frac{π}{2} + π n}$ , for any integer $n$

Set-Builder Notation:

${x | x \neq \frac{π}{2} + π n}$ , for any integer $n$

Step 2

Since the domain is not all real numbers, $\tan (x)$ is not continuous over all real numbers.

Not continuous

Step 3