Trigonometry Examples

$f (x) = - 7 \csc (\frac{1}{3} x + \frac{π}{12})$

Step 1

Set the argument in $\csc (\frac{1}{3} x + \frac{π}{12})$ equal to $π n$ to find where the expression is undefined.

$\frac{1}{3} x + \frac{π}{12} = π n$ , for any integer $n$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + \frac{π}{12} = π n$

Step 2.2

Subtract $\frac{π}{12}$ from both sides of the equation.

$\frac{x}{3} = π n - \frac{π}{12}$

Step 2.3

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (π n - \frac{π}{12})$

Step 2.4

Simplify both sides of the equation.

Tap for more steps...

Step 2.4.1

Simplify the left side.

Tap for more steps...

Step 2.4.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 (π n - \frac{π}{12})$

Step 2.4.1.1.2

Rewrite the expression.

$x = 3 (π n - \frac{π}{12})$

Step 2.4.2

Simplify the right side.

Tap for more steps...

Step 2.4.2.1

Simplify $3 (π n - \frac{π}{12})$ .

Tap for more steps...

Step 2.4.2.1.1

Apply the distributive property.

$x = 3 (π n) + 3 (- \frac{π}{12})$

Step 2.4.2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.2.1.2.1

Move the leading negative in $- \frac{π}{12}$ into the numerator.

$x = 3 π n + 3 \frac{- π}{12}$

Step 2.4.2.1.2.2

Factor $3$ out of $12$ .

$x = 3 π n + 3 \frac{- π}{3 (4)}$

Step 2.4.2.1.2.3

Cancel the common factor.

$x = 3 π n + 3 \frac{- π}{3 \cdot 4}$

Step 2.4.2.1.2.4

Rewrite the expression.

$x = 3 π n + \frac{- π}{4}$

Step 2.4.2.1.3

Move the negative in front of the fraction.

$x = 3 π n - \frac{π}{4}$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${x | x = 3 π n - \frac{π}{4}}$ $n$ , for any integer $n$

Step 4