Trigonometry Examples

f (x) = \tan (x)

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

Step 1

Set the argument in

\tan (x)

$\tan (x)$ equal to

\frac{π}{2} + π n

$\frac{π}{2} + π n$ to find where the expression is undefined.

x = \frac{π}{2} + π n

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

n

$n$

Step 2

The domain is all values of

x

$x$ that make the expression defined.

Set-Builder Notation:

{x | x \neq \frac{π}{2} + π n}

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

n

$n$

Step 3

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$

Set-Builder Notation:

{y | y \in ℝ}

${y | y \in ℝ}$

Step 4

Determine the domain and range.

Domain:

{x | x \neq \frac{π}{2} + π n}

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

n

$n$

Range:

(- \infty, \infty), {y | y \in ℝ}

$(- \infty, \infty), {y | y \in ℝ}$

Step 5

f (x) = \tan x

$f (x) = \tan x$

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