Trigonometry Examples

$\sin (- x) \cot (x - π)$

Step 1

Since $\sin (- x)$ is an odd function, rewrite $\sin (- x)$ as $- \sin (x)$ .

$- \sin (x) \cot (x - π)$

Step 2

Rewrite $\cot (x - π)$ in terms of sines and cosines.

$- \sin (x) \frac{\cos (x - π)}{\sin (x - π)}$

Step 3

Combine $\frac{\cos (x - π)}{\sin (x - π)}$ and $\sin (x)$ .

$- \frac{\cos (x - π) \sin (x)}{\sin (x - π)}$

Step 4

Separate fractions.

$- (\frac{\sin (x)}{1} \cdot \frac{\cos (x - π)}{\sin (x - π)})$

Step 5

Convert from $\frac{\cos (x - π)}{\sin (x - π)}$ to $\cot (x - π)$ .

$- (\frac{\sin (x)}{1} \cot (x - π))$

Step 6

Divide $\sin (x)$ by $1$ .

$- \sin (x) \cot (x - π)$