Algebra Examples Algebra Concepts and Expressions

Evaluate Using the Given Value

$\cot (3 x)$ , $x = \frac{2 π}{3}$

Step 1

Replace the variable $x$ with $\frac{2 π}{3}$ in the expression.

$\cot (3 (\frac{2 π}{3}))$

Step 2

Rewrite $\cot (3 (\frac{2 π}{3}))$ in terms of sines and cosines.

$\frac{\cos (3 \frac{2 π}{3})}{\sin (3 \frac{2 π}{3})}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{\cos (3 \frac{2 π}{3})}{\sin (3 \frac{2 π}{3})}$

Step 3.2

Rewrite the expression.

$\frac{\cos (3 \frac{2 π}{3})}{\sin (2 π)}$

Step 4

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{\cos (3 \frac{2 π}{3})}{\sin (0)}$

Step 5

The exact value of $\sin (0)$ is $0$ .

$\frac{\cos (3 \frac{2 π}{3})}{0}$

Step 6

The expression contains a division by $0$ . The expression is undefined.

Undefined

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Evaluate Using the Given Value

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