Trigonometry Examples

f (x) = \frac{1}{2} cot (x)

$f (x) = \frac{1}{2} \cot (x)$

Step 1

Set the argument in

cot (x)

$\cot (x)$ equal to

π n

$π n$ to find where the expression is undefined.

x = π n

$x = π n$ , 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 π n}

${x | x \neq π n}$ , 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:

${y | y \in ℝ}$

Step 4

Determine the domain and range.

Domain:

${x | x \neq π n}$ , for any integer

$n$

Range:

$(- \infty, \infty), {y | y \in ℝ}$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$