Precalculus Examples

$\frac{\cos (x)}{\sec (x) + \tan (x)}$

Step 1

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

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

Step 2

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

$x \approx \frac{3 π}{2} + 6.28318538 n$ , for any integer $n$

Step 3

Set the argument in $\sec (x)$ 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

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

Set-Builder Notation:

${x | x \neq \frac{3 π}{2} + 6.28318538 n, x \neq \frac{π}{2} + π n}$ , for any integer $n$

Step 5