Trigonometry Examples

$y = \cot (\frac{1}{6} x)$

Step 1

Set the argument in $\cot (\frac{1}{6} x)$ equal to $π n$ to find where the expression is undefined.

$\frac{1}{6} x = π n$ , for any integer $n$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} x) = 6 (π n)$

Step 2.2

Simplify both sides of the equation.

Tap for more steps...

Step 2.2.1

Simplify the left side.

Tap for more steps...

Step 2.2.1.1

Simplify $6 (\frac{1}{6} x)$ .

Tap for more steps...

Step 2.2.1.1.1

Combine $\frac{1}{6}$ and $x$ .

$6 \frac{x}{6} = 6 (π n)$

Step 2.2.1.1.2

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

$6 \frac{x}{6} = 6 (π n)$

Step 2.2.1.1.2.2

Rewrite the expression.

$x = 6 (π n)$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Remove parentheses.

$x = 6 π n$

Step 3

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

Set-Builder Notation:

${x | x \neq 6 π n}$ , for any integer $n$

Step 4