Calculus Examples

$\sec (\sin (x))$

Step 1

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

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

Step 2

Solve for $x$ .

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Step 2.1

Reorder $\frac{π}{2}$ and $π n$ .

$\sin (x) = π n + \frac{π}{2}$

Step 2.2

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

$x = \arcsin (π n + \frac{π}{2})$

Step 3

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

Set-Builder Notation:

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

Step 4