Finite Math Examples

$\frac{\tan (x)}{\tan (x) + \cot (x)}$

Step 1

Set the denominator in $\frac{\tan (x)}{\tan (x) + \cot (x)}$ equal to $0$ to find where the expression is undefined.

$\tan (x) + \cot (x) = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3

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

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

Step 4

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

$x = π n$ , for any integer $n$

Step 5

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

Set-Builder Notation:

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

Step 6