Trigonometry Examples

$\frac{- 4 \cdot 3 + 2 (2)}{2 i \sqrt{3} \cdot \sqrt{13}}$

Step 1

Cancel the common factor of $- 4 \cdot 3 + 2 (2)$ and $2$ .

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Step 1.1

Factor $2$ out of $- 4 \cdot 3$ .

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

Step 1.2

Factor $2$ out of $2 (- 2 \cdot 3) + 2 (2)$ .

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

Step 1.3

Cancel the common factors.

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Step 1.3.1

Factor $2$ out of $2 i \sqrt{3} \cdot \sqrt{13}$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

$\frac{- 2 \cdot 3 + 2}{i \sqrt{3} \cdot \sqrt{13}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 2$ by $3$ .

$\frac{- 6 + 2}{i \sqrt{3} \cdot \sqrt{13}}$

Step 2.2

Add $- 6$ and $2$ .

$\frac{- 4}{i \sqrt{3} \cdot \sqrt{13}}$

Step 3

Simplify the denominator.

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Step 3.1

Combine using the product rule for radicals.

$\frac{- 4}{i \sqrt{13 \cdot 3}}$

Step 3.2

Multiply $13$ by $3$ .

$\frac{- 4}{i \sqrt{39}}$

Step 4

Move the negative in front of the fraction.

$- \frac{4}{i \sqrt{39}}$

Step 5

Multiply $\frac{4}{i \sqrt{39}}$ by $\frac{\sqrt{39}}{\sqrt{39}}$ .

$- (\frac{4}{i \sqrt{39}} \cdot \frac{\sqrt{39}}{\sqrt{39}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{4}{i \sqrt{39}}$ by $\frac{\sqrt{39}}{\sqrt{39}}$ .

$- \frac{4 \sqrt{39}}{i \sqrt{39} \sqrt{39}}$

Step 6.2

Move $\sqrt{39}$ .

$- \frac{4 \sqrt{39}}{i (\sqrt{39} \sqrt{39})}$

Step 6.3

Raise $\sqrt{39}$ to the power of $1$ .

$- \frac{4 \sqrt{39}}{i ({\sqrt{39}}^{1} \sqrt{39})}$

Step 6.4

Raise $\sqrt{39}$ to the power of $1$ .

$- \frac{4 \sqrt{39}}{i ({\sqrt{39}}^{1} {\sqrt{39}}^{1})}$

Step 6.5

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

$- \frac{4 \sqrt{39}}{i {\sqrt{39}}^{1 + 1}}$

Step 6.6

Add $1$ and $1$ .

$- \frac{4 \sqrt{39}}{i {\sqrt{39}}^{2}}$

Step 6.7

Rewrite ${\sqrt{39}}^{2}$ as $39$ .

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Step 6.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{39}$ as $39^{\frac{1}{2}}$ .

$- \frac{4 \sqrt{39}}{i {(39^{\frac{1}{2}})}^{2}}$

Step 6.7.2

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

$- \frac{4 \sqrt{39}}{i \cdot 39^{\frac{1}{2} \cdot 2}}$

Step 6.7.3

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

$- \frac{4 \sqrt{39}}{i \cdot 39^{\frac{2}{2}}}$

Step 6.7.4

Cancel the common factor of $2$ .

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Step 6.7.4.1

Cancel the common factor.

$- \frac{4 \sqrt{39}}{i \cdot 39^{\frac{2}{2}}}$

Step 6.7.4.2

Rewrite the expression.

$- \frac{4 \sqrt{39}}{i \cdot 39^{1}}$

Step 6.7.5

Evaluate the exponent.

$- \frac{4 \sqrt{39}}{i \cdot 39}$

Step 7

Move $39$ to the left of $i$ .

$- \frac{4 \sqrt{39}}{39 i}$