Trigonometry Examples

$\frac{\cot (x)}{\sin (x)}$

Step 1

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

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

Step 2

Rewrite $\frac{\frac{\cos (x)}{\sin (x)}}{\sin (x)}$ as a product.

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

Step 3

Multiply $\frac{\cos (x)}{\sin (x)}$ by $\frac{1}{\sin (x)}$ .

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

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

Separate fractions.

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

Step 7

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

$\frac{1}{\sin (x)} \cot (x)$

Step 8

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x) \cot (x)$