Trigonometry Examples

$\cot (3 x) = \sqrt{3}$

Step 1

Subtract $\sqrt{3}$ from both sides of the equation.

$\cot (3 x) - \sqrt{3} = 0$

Step 2

Set the argument in $\cot (3 x)$ equal to $π n$ to find where the expression is undefined.

$3 x = π n$ , for any integer $n$

Step 3

Divide each term in $3 x = π n$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 x = π n$ by $3$ .

$\frac{3 x}{3} = \frac{π n}{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{π n}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{π n}{3}$

Step 4

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 $0$ .

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

Step 5