Precalculus Examples

$\sin (x) \cot (y)$

Step 1

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

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

Step 2

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

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

Step 3

Separate fractions.

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

Step 4

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

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

Step 5

Write $\sin (x)$ as a fraction with denominator $1$ .

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

Step 6

Simplify.

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Step 6.1

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

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

Step 6.2

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

$\frac{\cos (y)}{1} (\sin (x) \csc (y))$

Step 7

Divide $\cos (y)$ by $1$ .

$\cos (y) \sin (x) \csc (y)$