Trigonometry Examples

$\cot (3 x)$ , $x = \frac{2 π}{3}$

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

$\cot (3 (\frac{2 π}{3}))$

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

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

Cancel the common factor of $3$ .

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Write $3$ as a fraction with denominator $1$ .

$\frac{\cos (3 \frac{2 π}{3})}{\sin (\frac{3}{1} \cdot \frac{2 π}{3})}$

Factor out the greatest common factor $3$ .

$\frac{\cos (3 \frac{2 π}{3})}{\sin (\frac{3 \cdot 1}{1} \cdot \frac{2 π}{3 \cdot 1})}$

Cancel the common factor.

$\frac{\cos (3 \frac{2 π}{3})}{\sin (\frac{3 \cdot 1}{1} \cdot \frac{2 π}{3 \cdot 1})}$

Rewrite the expression.

$\frac{\cos (3 \frac{2 π}{3})}{\sin (\frac{1}{1} \cdot \frac{2 π}{1})}$

Simplify.

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Multiply $\frac{1}{1}$ and $\frac{2 π}{1}$ .

$\frac{\cos (3 \frac{2 π}{3})}{\sin (\frac{2 π}{1})}$

Divide $2 π$ by $1$ .

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

$2 π$ is a full rotation so replace with $0$ .

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

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

$\frac{\cos (3 \frac{2 π}{3})}{0}$

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

Undefined

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