Trigonometry Examples

$\csc (x \cdot 180)$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the argument in $\csc (x \cdot 180)$ equal to $π n$ to find where the expression is undefined.

$x \cdot 180 = π n$ , for any integer $n$

Step 1.2

Divide each term in $x \cdot 180 = π n$ by $180$ and simplify.

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Step 1.2.1

Divide each term in $x \cdot 180 = π n$ by $180$ .

$\frac{x \cdot 180}{180} = \frac{π n}{180}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $180$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{x \cdot 180}{180} = \frac{π n}{180}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{π n}{180}$

Step 1.3

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

Set-Builder Notation:

${x | x \neq \frac{π n}{180}}$ , for any integer $n$

Set-Builder Notation:

${x | x \neq \frac{π n}{180}}$ , for any integer $n$

Step 2

Since the domain is not all real numbers, $\csc (x \cdot 180)$ is not continuous over all real numbers.

Not continuous

Step 3