Trigonometry Examples

$2 \cdot (\frac{3}{\sqrt{13}}) \cdot (\frac{2}{\sqrt{13}})$

Step 1

Multiply $\frac{3}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$2 \cdot (\frac{3}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}) \cdot \frac{2}{\sqrt{13}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{3}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$2 \cdot \frac{3 \sqrt{13}}{\sqrt{13} \sqrt{13}} \cdot \frac{2}{\sqrt{13}}$

Step 2.2

Raise $\sqrt{13}$ to the power of $1$ .

$2 \cdot \frac{3 \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}} \cdot \frac{2}{\sqrt{13}}$

Step 2.3

Raise $\sqrt{13}$ to the power of $1$ .

$2 \cdot \frac{3 \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}} \cdot \frac{2}{\sqrt{13}}$

Step 2.4

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

$2 \cdot \frac{3 \sqrt{13}}{{\sqrt{13}}^{1 + 1}} \cdot \frac{2}{\sqrt{13}}$

Step 2.5

Add $1$ and $1$ .

$2 \cdot \frac{3 \sqrt{13}}{{\sqrt{13}}^{2}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$2 \cdot \frac{3 \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot \frac{3 \sqrt{13}}{13^{\frac{1}{2} \cdot 2}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6.3

Combine $\frac{1}{2}$ and $2$ .

$2 \cdot \frac{3 \sqrt{13}}{13^{\frac{2}{2}}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$2 \cdot \frac{3 \sqrt{13}}{13^{\frac{2}{2}}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6.4.2

Rewrite the expression.

$2 \cdot \frac{3 \sqrt{13}}{13^{1}} \cdot \frac{2}{\sqrt{13}}$

Step 2.6.5

Evaluate the exponent.

$2 \cdot \frac{3 \sqrt{13}}{13} \cdot \frac{2}{\sqrt{13}}$

Step 3

Multiply $2 \frac{3 \sqrt{13}}{13}$ .

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Step 3.1

Combine $2$ and $\frac{3 \sqrt{13}}{13}$ .

$\frac{2 (3 \sqrt{13})}{13} \cdot \frac{2}{\sqrt{13}}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{6 \sqrt{13}}{13} \cdot \frac{2}{\sqrt{13}}$

Step 4

Cancel the common factor of $\sqrt{13}$ .

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Step 4.1

Factor $\sqrt{13}$ out of $6 \sqrt{13}$ .

$\frac{\sqrt{13} \cdot 6}{13} \cdot \frac{2}{\sqrt{13}}$

Step 4.2

Cancel the common factor.

$\frac{\sqrt{13} \cdot 6}{13} \cdot \frac{2}{\sqrt{13}}$

Step 4.3

Rewrite the expression.

$\frac{6}{13} \cdot 2$

Step 5

Combine $\frac{6}{13}$ and $2$ .

$\frac{6 \cdot 2}{13}$

Step 6

Multiply $6$ by $2$ .

$\frac{12}{13}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{13}$

Decimal Form:

$0.\overline{923076}$