Trigonometry Examples

$2 (- \frac{9}{\sqrt{19}}) (\frac{19}{- 62})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $- 62$ .

$2 (- \frac{9}{\sqrt{19}}) \cdot \frac{19}{2 (- 31)}$

Step 1.2

Cancel the common factor.

$2 (- \frac{9}{\sqrt{19}}) \cdot \frac{19}{2 \cdot - 31}$

Step 1.3

Rewrite the expression.

$- \frac{9}{\sqrt{19}} \cdot \frac{19}{- 31}$

Step 2

Multiply $\frac{19}{- 31}$ by $\frac{9}{\sqrt{19}}$ .

$- \frac{19 \cdot 9}{- 31 \sqrt{19}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $19$ by $9$ .

$- \frac{171}{- 31 \sqrt{19}}$

Step 3.2

Move the negative in front of the fraction.

$- - \frac{171}{31 \sqrt{19}}$

Step 4

Multiply $\frac{171}{31 \sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$- - (\frac{171}{31 \sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}})$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{171}{31 \sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$- - \frac{171 \sqrt{19}}{31 \sqrt{19} \sqrt{19}}$

Step 5.2

Move $\sqrt{19}$ .

$- - \frac{171 \sqrt{19}}{31 (\sqrt{19} \sqrt{19})}$

Step 5.3

Raise $\sqrt{19}$ to the power of $1$ .

$- - \frac{171 \sqrt{19}}{31 ({\sqrt{19}}^{1} \sqrt{19})}$

Step 5.4

Raise $\sqrt{19}$ to the power of $1$ .

$- - \frac{171 \sqrt{19}}{31 ({\sqrt{19}}^{1} {\sqrt{19}}^{1})}$

Step 5.5

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

$- - \frac{171 \sqrt{19}}{31 {\sqrt{19}}^{1 + 1}}$

Step 5.6

Add $1$ and $1$ .

$- - \frac{171 \sqrt{19}}{31 {\sqrt{19}}^{2}}$

Step 5.7

Rewrite ${\sqrt{19}}^{2}$ as $19$ .

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Step 5.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{19}$ as $19^{\frac{1}{2}}$ .

$- - \frac{171 \sqrt{19}}{31 {(19^{\frac{1}{2}})}^{2}}$

Step 5.7.2

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

$- - \frac{171 \sqrt{19}}{31 \cdot 19^{\frac{1}{2} \cdot 2}}$

Step 5.7.3

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

$- - \frac{171 \sqrt{19}}{31 \cdot 19^{\frac{2}{2}}}$

Step 5.7.4

Cancel the common factor of $2$ .

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Step 5.7.4.1

Cancel the common factor.

$- - \frac{171 \sqrt{19}}{31 \cdot 19^{\frac{2}{2}}}$

Step 5.7.4.2

Rewrite the expression.

$- - \frac{171 \sqrt{19}}{31 \cdot 19^{1}}$

Step 5.7.5

Evaluate the exponent.

$- - \frac{171 \sqrt{19}}{31 \cdot 19}$

Step 6

Cancel the common factor of $171$ and $19$ .

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Step 6.1

Factor $19$ out of $171 \sqrt{19}$ .

$- - \frac{19 (9 \sqrt{19})}{31 \cdot 19}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $19$ out of $31 \cdot 19$ .

$- - \frac{19 (9 \sqrt{19})}{19 \cdot 31}$

Step 6.2.2

Cancel the common factor.

$- - \frac{19 (9 \sqrt{19})}{19 \cdot 31}$

Step 6.2.3

Rewrite the expression.

$- - \frac{9 \sqrt{19}}{31}$

Step 7

Multiply $- - \frac{9 \sqrt{19}}{31}$ .

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Step 7.1

Multiply $- 1$ by $- 1$ .

$1 \frac{9 \sqrt{19}}{31}$

Step 7.2

Multiply $\frac{9 \sqrt{19}}{31}$ by $1$ .

$\frac{9 \sqrt{19}}{31}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{9 \sqrt{19}}{31}$

Decimal Form:

$1.26548679 \dots$