Trigonometry Examples

$r \sin^{2} (x) = 12 \cos (x)$

Step 1

Divide each term in $r \sin^{2} (x) = 12 \cos (x)$ by $\sin^{2} (x)$ .

$\frac{r \sin^{2} (x)}{\sin^{2} (x)} = \frac{12 \cos (x)}{\sin^{2} (x)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\sin^{2} (x)$ .

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Step 2.1.1

Cancel the common factor.

$\frac{r \sin^{2} (x)}{\sin^{2} (x)} = \frac{12 \cos (x)}{\sin^{2} (x)}$

Step 2.1.2

Divide $r$ by $1$ .

$r = \frac{12 \cos (x)}{\sin^{2} (x)}$

Step 3

Simplify the right side.

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Step 3.1

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

$r = \frac{12 \cos (x)}{\sin (x) \sin (x)}$

Step 3.2

Separate fractions.

$r = \frac{12}{\sin (x)} \cdot \frac{\cos (x)}{\sin (x)}$

Step 3.3

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

$r = \frac{12}{\sin (x)} \cot (x)$

Step 3.4

Separate fractions.

$r = \frac{12}{1} \cdot \frac{1}{\sin (x)} \cot (x)$

Step 3.5

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

$r = \frac{12}{1} \csc (x) \cot (x)$

Step 3.6

Divide $12$ by $1$ .

$r = 12 \csc (x) \cot (x)$