Trigonometry Examples

$\frac{9 \sqrt{2} (\frac{\sqrt{3}}{2})}{\frac{\sqrt{2}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$9 \sqrt{2} \frac{\sqrt{3}}{2} \frac{2}{\sqrt{2}}$

Step 2

Cancel the common factor of $\sqrt{2}$ .

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Step 2.1

Factor $\sqrt{2}$ out of $9 \sqrt{2} \frac{\sqrt{3}}{2}$ .

$\sqrt{2} (9 \frac{\sqrt{3}}{2}) \frac{2}{\sqrt{2}}$

Step 2.2

Cancel the common factor.

$\sqrt{2} (9 \frac{\sqrt{3}}{2}) \frac{2}{\sqrt{2}}$

Step 2.3

Rewrite the expression.

$9 \frac{\sqrt{3}}{2} \cdot 2$

Step 3

Combine $9$ and $\frac{\sqrt{3}}{2}$ .

$\frac{9 \sqrt{3}}{2} \cdot 2$

Step 4

Combine $\frac{9 \sqrt{3}}{2}$ and $2$ .

$\frac{9 \sqrt{3} \cdot 2}{2}$

Step 5

Multiply $2$ by $9$ .

$\frac{18 \sqrt{3}}{2}$

Step 6

Cancel the common factor of $18$ and $2$ .

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Step 6.1

Factor $2$ out of $18 \sqrt{3}$ .

$\frac{2 (9 \sqrt{3})}{2}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2$ .

$\frac{2 (9 \sqrt{3})}{2 (1)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (9 \sqrt{3})}{2 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{9 \sqrt{3}}{1}$

Step 6.2.4

Divide $9 \sqrt{3}$ by $1$ .

$9 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{3}$

Decimal Form:

$15.58845726 \dots$