Trigonometry Examples

y = \csc (x)

$y = \csc (x)$

Step 1

Set the argument in

\csc (x)

$\csc (x)$ 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, - 1] \cup [1, \infty)

$(- \infty, - 1] \cup [1, \infty)$

Set-Builder Notation:

{y | y \leq - 1, y \geq 1}

${y | y \leq - 1, y \geq 1}$

Step 4

Determine the domain and range.

Domain:

{x | x \neq π n}

${x | x \neq π n}$ , for any integer

n

$n$

Range:

(- \infty, - 1] \cup [1, \infty), {y | y \leq - 1, y \geq 1}

$(- \infty, - 1] \cup [1, \infty), {y | y \leq - 1, y \geq 1}$

Step 5