Trigonometry Examples

$\sin (- x) \tan (x)$

Step 1

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

$- \sin (x) \tan (x)$

Step 2

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Step 3

Multiply $- \sin (x) \frac{\sin (x)}{\cos (x)}$ .

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Step 3.1

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

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

Step 3.2

Raise $\sin (x)$ to the power of $1$ .

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

Step 3.3

Raise $\sin (x)$ to the power of $1$ .

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

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{{\sin (x)}^{1 + 1}}{\cos (x)}$

Step 3.5

Add $1$ and $1$ .

$- \frac{\sin^{2} (x)}{\cos (x)}$

Step 4

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

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

Step 5

Separate fractions.

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

Step 6

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$- (\frac{\sin (x)}{1} \tan (x))$

Step 7

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

$- \sin (x) \tan (x)$