Trigonometry Examples

$\tan (arccsc (x))$

Step 1

Set the argument in $\tan (arccsc (x))$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

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

Step 2

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

$x = \csc (\frac{π}{2} + π n)$

Step 3

Set the argument in $arccsc (x)$ greater than $- 1$ to find where the expression is undefined.

$x > - 1$

Step 4

Set the argument in $arccsc (x)$ less than $1$ to find where the expression is undefined.

$x < 1$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${x | x = \csc (\frac{π}{2} + π n)}$ $n$ , for any integer $n$

Step 6