Trigonometry Examples

$f (x) = \tan (x)$

Step 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 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 $n$

Step 3

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 4

Determine the domain and range.

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

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 5