Precalculus Examples

$\csc (\arccos (x))$

Step 1

Set the argument in $\arccos (x)$ greater than or equal to $- 1$ to find where the expression is defined.

$x \geq - 1$

Step 2

Set the argument in $\arccos (x)$ less than or equal to $1$ to find where the expression is defined.

$x \leq 1$

Step 3

Set the argument in $\csc (\arccos (x))$ equal to $π n$ to find where the expression is undefined.

$\arccos (x) = π n$ , for any integer $n$

Step 4

Take the inverse arccosine of both sides of the equation to extract $x$ from inside the arccosine.

$x = \cos (π n)$

Step 5

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

Set-Builder Notation:

${x | - 1 \leq x \leq 1, x \neq \cos (π n)}$

Step 6